#1**+1 **

1/2*(x + 2)*(2x - 3)*sin(45) =4sqrt(2), solve for x

Solve for x:

(2 x^2 + x - 6)/(2 sqrt(2)) = 4 sqrt(2)

Multiply both sides by 2 sqrt(2):

2 x^2 + x - 6 = 16

Divide both sides by 2:

x^2 + x/2 - 3 = 8

Add 3 to both sides:

x^2 + x/2 = 11

Add 1/16 to both sides:

x^2 + x/2 + 1/16 = 177/16

Write the left hand side as a square:

(x + 1/4)^2 = 177/16

Take the square root of both sides:

x + 1/4 = sqrt(177)/4 or x + 1/4 = -sqrt(177)/4

Subtract 1/4 from both sides:

x = sqrt(177)/4 - 1/4 or x + 1/4 = -sqrt(177)/4

Subtract 1/4 from both sides:

**x = sqrt(177)/4 - 1/4 =~3.076**

Guest Apr 6, 2018