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Solve the quadratic equation 5x2+75x=0 by factoring out the GCF.(1 point)

Responses

The solutions are x=−15 and x=−5.
The solutions are x equals negative 15 and x equals negative 5 .

The solutions are x=0 and x=5.
The solutions are x equals 0 and x equals 5 .

The solutions are x=0 and x=15.
The solutions are x equals 0 and x equals 15 .

The solutions are x=−15 and x=0.

7 answers

To solve the quadratic equation \(5x^2 + 75x = 0\) by factoring out the greatest common factor (GCF), we first identify the GCF, which is \(5x\).

Factoring out \(5x\) from the equation gives us:

\[ 5x(x + 15) = 0 \]

To find the solutions, we can set each factor equal to zero:

  1. \(5x = 0\) leads to: \[ x = 0 \]

  2. \(x + 15 = 0\) leads to: \[ x = -15 \]

Thus, the solutions to the equation are:

  • \(x = 0\)
  • \(x = -15\)

The correct response is: The solutions are \(x = -15\) and \(x = 0\).

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 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 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 0

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

A>B>C>D

To solve the quadratic equation \(7x^2 = 56x\), we can follow these steps:

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

  2. Factor out the GCF: The GCF in this equation is \(7x\): \[ 7x(x - 8) = 0 \]

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

  4. Find the solutions:

    • From \(7x = 0\), we get: \[ x = 0 \]
    • From \(x - 8 = 0\), we get: \[ x = 8 \]

Thus, the solutions to the equation are \(x = 0\) and \(x = 8\).

Now, looking at the options provided, the correct table 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 \(x=8\)

So, this corresponds to the second response:

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 0 and x equals 8.

Therefore, the correct choice is A > B > C > D.

what is the answer

The correct table of steps to factor out the GCF and solve the quadratic equation \(7x^2 = 56x\) 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 \(x = 8\)

Based on the choices provided, this corresponds to the following option:

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 0 and x equals 8.

So, the answer is the second response.

a.b.c.d?

The correct option corresponds to:

B

So the answer is: B.