x^2+0.96x-76.8=0

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Solution for x^2+0.96x-76.8=0 equation: 


Simplifying
x2 + 0.96x + -76.8 = 0

Reorder the terms:
-76.8 + 0.96x + x2 = 0

Solving
-76.8 + 0.96x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '76.8' to each side of the equation.
-76.8 + 0.96x + 76.8 + x2 = 0 + 76.8

Reorder the terms:
-76.8 + 76.8 + 0.96x + x2 = 0 + 76.8

Combine like terms: -76.8 + 76.8 = 0.0
0.0 + 0.96x + x2 = 0 + 76.8
0.96x + x2 = 0 + 76.8

Combine like terms: 0 + 76.8 = 76.8
0.96x + x2 = 76.8

The x term is 0.96x.  Take half its coefficient (0.48).
Square it (0.2304) and add it to both sides.

Add '0.2304' to each side of the equation.
0.96x + 0.2304 + x2 = 76.8 + 0.2304

Reorder the terms:
0.2304 + 0.96x + x2 = 76.8 + 0.2304

Combine like terms: 76.8 + 0.2304 = 77.0304
0.2304 + 0.96x + x2 = 77.0304

Factor a perfect square on the left side:
(x + 0.48)(x + 0.48) = 77.0304

Calculate the square root of the right side: 8.776696417

Break this problem into two subproblems by setting 
(x + 0.48) equal to 8.776696417 and -8.776696417.


Subproblem 1
x + 0.48 = 8.776696417

Simplifying
x + 0.48 = 8.776696417

Reorder the terms:
0.48 + x = 8.776696417

Solving
0.48 + x = 8.776696417

Solving for variable 'x'.

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

Add '-0.48' to each side of the equation.
0.48 + -0.48 + x = 8.776696417 + -0.48

Combine like terms: 0.48 + -0.48 = 0.00
0.00 + x = 8.776696417 + -0.48
x = 8.776696417 + -0.48

Combine like terms: 8.776696417 + -0.48 = 8.296696417
x = 8.296696417

Simplifying
x = 8.296696417


Subproblem 2
x + 0.48 = -8.776696417

Simplifying
x + 0.48 = -8.776696417

Reorder the terms:
0.48 + x = -8.776696417

Solving
0.48 + x = -8.776696417

Solving for variable 'x'.

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

Add '-0.48' to each side of the equation.
0.48 + -0.48 + x = -8.776696417 + -0.48

Combine like terms: 0.48 + -0.48 = 0.00
0.00 + x = -8.776696417 + -0.48
x = -8.776696417 + -0.48

Combine like terms: -8.776696417 + -0.48 = -9.256696417
x = -9.256696417

Simplifying
x = -9.256696417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.296696417, -9.256696417}

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