Answer: [tex]\bold{x=\bigg\{4,-\dfrac{2}{7}}\bigg\}[/tex]
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 [tex]=-\dfrac{2}{7}[/tex]
