5x^2+8x-672=0

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Solution for 5x^2+8x-672=0 equation: 


Simplifying
5x2 + 8x + -672 = 0

Reorder the terms:
-672 + 8x + 5x2 = 0

Solving
-672 + 8x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-134.4 + 1.6x + x2 = 0

Move the constant term to the right:

Add '134.4' to each side of the equation.
-134.4 + 1.6x + 134.4 + x2 = 0 + 134.4

Reorder the terms:
-134.4 + 134.4 + 1.6x + x2 = 0 + 134.4

Combine like terms: -134.4 + 134.4 = 0.0
0.0 + 1.6x + x2 = 0 + 134.4
1.6x + x2 = 0 + 134.4

Combine like terms: 0 + 134.4 = 134.4
1.6x + x2 = 134.4

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 134.4 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 134.4 + 0.64

Combine like terms: 134.4 + 0.64 = 135.04
0.64 + 1.6x + x2 = 135.04

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 135.04

Calculate the square root of the right side: 11.620671237

Break this problem into two subproblems by setting 
(x + 0.8) equal to 11.620671237 and -11.620671237.


Subproblem 1
x + 0.8 = 11.620671237

Simplifying
x + 0.8 = 11.620671237

Reorder the terms:
0.8 + x = 11.620671237

Solving
0.8 + x = 11.620671237

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 11.620671237 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 11.620671237 + -0.8
x = 11.620671237 + -0.8

Combine like terms: 11.620671237 + -0.8 = 10.820671237
x = 10.820671237

Simplifying
x = 10.820671237


Subproblem 2
x + 0.8 = -11.620671237

Simplifying
x + 0.8 = -11.620671237

Reorder the terms:
0.8 + x = -11.620671237

Solving
0.8 + x = -11.620671237

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -11.620671237 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -11.620671237 + -0.8
x = -11.620671237 + -0.8

Combine like terms: -11.620671237 + -0.8 = -12.420671237
x = -12.420671237

Simplifying
x = -12.420671237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.820671237, -12.420671237}

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