Question

7X²-26X-8=0 Solving polynomial equations with factoring, algebra. Please help me!

Answer 1

Answer:   $\bold{x=\bigg\{4,-\dfrac{2}{7}}\bigg\}$

Step-by-step explanation:

7x² - 26x - 8 = 0            

Find two numbers whose product equals (7)(-8) and sum equals -26.

                        -28 × 2 = 56, -28 + 2 = -26

Replace -26x with -28x + 2x:      7x² - 28x + 2x - 8 = 0

Factor the left two terms & right two terms:    7x(x - 4) + 2(x - 4) = 0

Notice that both sides have a common factor of (x - 4)  -->  This is one of the factors.  The other factor is what is on the outside of (x - 4) --> 7x + 2

Rewrite the expression as two factors:   (x - 4)(7x + 2) = 0

set each factor equal to zero and solve for x.

              x - 4 = 0                7x + 2 = 0

                   x = 4                 7x       = -2

                                              x       $=-\dfrac{2}{7}$