Solve the following quadratic equation by factoring out the GCF: 52x^2+6x=0 2 x 2x

Question

Answer 1

To solve the quadratic equation

by factoring out the greatest common factor (GCF), follow these steps:1. **Identify the GCF of the terms**: The terms in the equation are

and

. The GCF of the coefficients

and

is

, and the GCF of the variable part

and

is

. Therefore, the GCF of the entire expression is

.2. **Factor out the GCF**: Factor

out of each term in the equation:

Simplify the expression inside the parentheses:

3. **Set each factor equal to zero**: The factored form of the equation is \(2x(26x + 3) = 0\). Set each factor equal to zero and solve for

:

4. **Solve each equation**: For

:

For

:

Subtract 3 from both sides:

Divide both sides by 26:

So, the solutions to the quadratic equation

are:

Question