Question

5x to the power of 2 -7x-6=0

Answer 1

Answer:

5x^2-7x-6=0

5x^2-10x+3x-6=0

5x(x-2)+3(x-2)=0

(x-2)(5x+3)=0

x-2=0

x=2

5x+3=0

5x= -3

x= -3/5

Answer 2

️Step by Step solution

5 x ^ { 2 } - 7 x - 6 = 0

• To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as 5x^{2}+ax+bx-6. To find a and b, set up a system to be solved.

a + b = - 7

ab = 5 ( -6 ) = - 30

• Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -30.

1,-30

2,-15

3,-10

5,-6

• Calculate the sum for each pair.

1-30=-29

1-30=-292-15=-13

1-30=-292-15=-133-10=-7

1-30=-292-15=-133-10=-7

5-6=-1

• The solution is the pair that gives sum -7.

a=-10

a=-10b=3

• Rewrite 5x² - 7x - 6 as (5x²- 10x) +(3x - 6)

$5x\left(x-2\right)+3\left(x-2\right)$

• Factor out common term x-2 by using distributive property

$\left(x-2\right)\left(5x+3\right)$

• To find equation solutions, solve x-2=0 and 5x+3=0.

$x=2 x=-\frac{3}{5}$