5x^2+3x-88=180

Solution for 5x^2+3x-88=180 equation:

Simplifying
5x2 + 3x + -88 = 180

Reorder the terms:
-88 + 3x + 5x2 = 180

Solving
-88 + 3x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
-88 + -180 + 3x + 5x2 = 180 + -180

Combine like terms: -88 + -180 = -268
-268 + 3x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-268 + 3x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-53.6 + 0.6x + x2 = 0

Move the constant term to the right:

Add '53.6' to each side of the equation.
-53.6 + 0.6x + 53.6 + x2 = 0 + 53.6

Reorder the terms:
-53.6 + 53.6 + 0.6x + x2 = 0 + 53.6

Combine like terms: -53.6 + 53.6 = 0.0
0.0 + 0.6x + x2 = 0 + 53.6
0.6x + x2 = 0 + 53.6

Combine like terms: 0 + 53.6 = 53.6
0.6x + x2 = 53.6

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 53.6 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 53.6 + 0.09

Combine like terms: 53.6 + 0.09 = 53.69
0.09 + 0.6x + x2 = 53.69

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 53.69

Calculate the square root of the right side: 7.327346041

Break this problem into two subproblems by setting 
(x + 0.3) equal to 7.327346041 and -7.327346041.

Subproblem 1
x + 0.3 = 7.327346041

Simplifying
x + 0.3 = 7.327346041

Reorder the terms:
0.3 + x = 7.327346041

Solving
0.3 + x = 7.327346041

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 7.327346041 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 7.327346041 + -0.3
x = 7.327346041 + -0.3

Combine like terms: 7.327346041 + -0.3 = 7.027346041
x = 7.027346041

Simplifying
x = 7.027346041

Subproblem 2
x + 0.3 = -7.327346041

Simplifying
x + 0.3 = -7.327346041

Reorder the terms:
0.3 + x = -7.327346041

Solving
0.3 + x = -7.327346041

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -7.327346041 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -7.327346041 + -0.3
x = -7.327346041 + -0.3

Combine like terms: -7.327346041 + -0.3 = -7.627346041
x = -7.627346041

Simplifying
x = -7.627346041

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.027346041, -7.627346041}