Question

Solve the equation by factoring 6x^2-17x+13=20x^2-32

Answer 1

6x^2 - 17x+13 = 20x^2 - 32

14x^2 + 17x - 45 = 0

(2x + 5)(7x - 9) = 0

2x + 5 = 0

2x = -5

x = -5/2

7x - 9 = 0

7x = 9

x = 9/7

Answer

x = -5/2 , 9/7

Answer 2

`x=(-5)/(2)`

`x=(9)/(7)`

Explanation:

`6x^2-17x+13=20x^2-32`

combine like terms and simplify the equation

Subtract 6x^2 from both sides

`6x^2-17x+13=20x^2-32`

`-17x+13=14x^2-32`

Add 17x on both sides

`13=14x^2+17x-32`

Now subtract 13 from both sides

`0=14x^2+17x-45`

Now we solve for x

Apply quadratic formula : a= 14, b= +17 and c= -45

`x=(-b+-√(b^2-4ac) )/(2a)`

`x=(-17+-√(17^2-4(14)(-45)) )/(2(14))`

`x=(-17+-53)/(28)`

Now make two equations

`x=(-17+53)/(28)=(-5)/(2)`

`x=(-17-53)/(28)=(9)/(7)`