Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x?(1 point)ResponsesPut the quadratic in standard formx−8=0Factor out the GCFNo GCFSet each factor equal to zerox−8=0The solutions arex=8 Put the quadratic in standard form x minus 8 equals 0 Factor out the GCF No GCF Set each factor equal to zero x minus 8 equals 0 The solutions are x equals 8Put the quadratic in standard form7x2−56x=0Factor out the GCF7x(x−8)=0Set each factor equal to zero7x=0 and x−8=0The solutions arex=0 and x=8Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals 0 and x equals 8Put the quadratic in standard form7x2−56x=0Factor out the GCF7x(x−8)=0Set each factor equal to zero7x=0 and x−8=0The solutions arex=−7 and x=8 Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals negative 7 and x equals 8Put the quadratic in standard form7x2+56x=0Factor out the GCF7x(x+8)=0Set each factor equal to zero7x=0 and x+8=0The solutions arex=−8 and x=0 Put the quadratic in standard form 7 x squared plus 56 x equals 0 Factor out the GCF 7 x left parenthesis x plus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x plus 8 equals 0 The solutions are x equals negative 8 and x equals 0Skip to navigation

asked anonymously

5 months ago

14 views

0

0

1 answer

To solve the quadratic equation $ 7x^2 = 56x $, we first need to rearrange it into standard form:

Put the quadratic in standard form: \[ 7x^2 - 56x = 0 \]

Factor out the GCF (Greatest Common Factor): \[ 7x(x - 8) = 0 \]

Set each factor equal to zero: \[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]

Solve for $ x $: \[ x = 0 \quad \text{and} \quad x = 8 \]

Therefore, the correct sequence of steps is:

Put the quadratic in standard form: $ 7x^2 - 56x = 0 $

Factor out the GCF: $ 7x(x - 8) = 0 $

Set each factor equal to zero: $ 7x = 0 $ and $ x - 8 = 0 $

The solutions are: $ x = 0 $ and $ x = 8 $

The option that matches these steps in the response list is:

Put the quadratic in standard form $ 7x^2 - 56x = 0 $ Factor out the GCF $ 7x(x - 8) = 0 $ Set each factor equal to zero $ 7x = 0 $ and $ x - 8 = 0 $ The solutions are $ x = 0 $ and $ x = 8 $.

answered by GPT-4o mini

0

0

Question

Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x?(1 point)ResponsesPut the quadratic in standard formx−8=0Factor out the GCFNo GCFSet each factor equal to zerox−8=0The solutions arex=8 Put the quadratic in standard form x minus 8 equals 0 Factor out the GCF No GCF Set each factor equal to zero x minus 8 equals 0 The solutions are x equals 8Put the quadratic in standard form7x2−56x=0Factor out the GCF7x(x−8)=0Set each factor equal to zero7x=0 and x−8=0The solutions arex=0 and x=8Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals 0 and x equals 8Put the quadratic in standard form7x2−56x=0Factor out the GCF7x(x−8)=0Set each factor equal to zero7x=0 and x−8=0The solutions arex=−7 and x=8 Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals negative 7 and x equals 8Put the quadratic in standard form7x2+56x=0Factor out the GCF7x(x+8)=0Set each factor equal to zero7x=0 and x+8=0The solutions arex=−8 and x=0 Put the quadratic in standard form 7 x squared plus 56 x equals 0 Factor out the GCF 7 x left parenthesis x plus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x plus 8 equals 0 The solutions are x equals negative 8 and x equals 0Skip to navigation

1 answer

To solve the quadratic equation $ 7x^2 = 56x $, we first need to rearrange it into standard form:

Put the quadratic in standard form: \[ 7x^2 - 56x = 0 \]
Factor out the GCF (Greatest Common Factor): \[ 7x(x - 8) = 0 \]
Set each factor equal to zero: \[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]
Solve for $ x $: \[ x = 0 \quad \text{and} \quad x = 8 \]

Therefore, the correct sequence of steps is:

Put the quadratic in standard form: $ 7x^2 - 56x = 0 $
Factor out the GCF: $ 7x(x - 8) = 0 $
Set each factor equal to zero: $ 7x = 0 $ and $ x - 8 = 0 $
The solutions are: $ x = 0 $ and $ x = 8 $

The option that matches these steps in the response list is:

Put the quadratic in standard form $ 7x^2 - 56x = 0 $ Factor out the GCF $ 7x(x - 8) = 0 $ Set each factor equal to zero $ 7x = 0 $ and $ x - 8 = 0 $ The solutions are $ x = 0 $ and $ x = 8 $.

GPT-4o mini · Answer

To solve the quadratic equation $ 7x^2 = 56x $, we first need to rearrange it into standard form: 1. **Put the quadratic in standard form**: $$ 7x^2 - 56x = 0 $$ 2. **Factor out the GCF** (Greatest Common Factor): $$ 7x(x - 8) = 0 $$ 3. **Set each factor equal to zero**: $$ 7x = 0 \quad \text{and} \quad x - 8 = 0 $$ 4. **Solve for $ x $**: $$ x = 0 \quad \text{and} \quad x = 8 $$ Therefore, the correct sequence of steps is: - Put the quadratic in standard form: $ 7x^2 - 56x = 0 $ - Factor out the GCF: $ 7x(x - 8) = 0 $ - Set each factor equal to zero: $ 7x = 0 $ and $ x - 8 = 0 $ - The solutions are: $ x = 0 $ and $ x = 8 $ The option that matches these steps in the response list is: **Put the quadratic in standard form $ 7x^2 - 56x = 0 $ Factor out the GCF $ 7x(x - 8) = 0 $ Set each factor equal to zero $ 7x = 0 $ and $ x - 8 = 0 $ The solutions are $ x = 0 $ and $ x = 8 $**.