To solve the quadratic equation \(7x^2 = 56x\), you need to move all terms to one side of the equation to put it in standard form, factor out the greatest common factor (GCF), and then set each factor equal to zero to find the solutions. Let's go through the correct steps:
1. Put the quadratic in standard form by moving the \(56x\) term to the left side of the equation:
\[ 7x^2 - 56x = 0 \]
2. Factor out the GCF, which in this case is \(7x\), since both terms are divisible by \(7x\):
\[ 7x(x - 8) = 0 \]
3. Set each factor equal to zero:
\[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]
4. Solve each equation for \(x\) to find the solutions:
\[ x = 0 \quad \text{from} \quad 7x = 0 \]
\[ x = 8 \quad \text{from} \quad x - 8 = 0 \]
Therefore, the solutions to the equation are \(x = 0\) and \(x = 8\).
The correct representation in the given options 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 incorrect options include suggesting that the solutions are \(x = -7\) or \(x = -8\), which are not correct for this equation. Only \(x = 0\) and \(x = 8\) satisfy the equation \(7x^2 = 56x\).
Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x?(1 point) Responses Put the quadratic in standard form x−8=0 Factor out the GCF No GCF Set each factor equal to zero x−8=0 The solutions are x=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 8 Put the quadratic in standard form 7x2−56x=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=−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 8 Put the quadratic in standard form 7x2−56x=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=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 8 Put the quadratic in standard form 7x2+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=−8 and x=0
1 answer
1 answer