Question

solve the equation by factoring. 8x^2 + 10x - 7 = 0 the solution set is {}. (type an integer or a simplified fraction. use a comma to separate answers as needed only once.)

Explanation:

Step1: Factor the quadratic equation

We need to factor \(8x^{2}+10x - 7=0\). We look for two numbers that multiply to \(8\times(-7)=- 56\) and add up to \(10\). The numbers are \(14\) and \(-4\).
Rewrite the middle - term: \(8x^{2}+14x-4x - 7 = 0\).
Group the terms: \((8x^{2}+14x)-(4x + 7)=0\).
Factor out the greatest common factor from each group: \(2x(4x + 7)-1(4x + 7)=0\).
Then \((2x - 1)(4x+7)=0\).

Step2: Set each factor equal to zero

If \(2x - 1=0\), then \(2x=1\), and \(x=\frac{1}{2}\).
If \(4x + 7=0\), then \(4x=-7\), and \(x=-\frac{7}{4}\).

Answer:

\(-\frac{7}{4},\frac{1}{2}\)