x^2+7.25x-84=0

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Solution for x^2+7.25x-84=0 equation: 


Simplifying
x2 + 7.25x + -84 = 0

Reorder the terms:
-84 + 7.25x + x2 = 0

Solving
-84 + 7.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 7.25x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 7.25x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 7.25x + x2 = 0 + 84
7.25x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
7.25x + x2 = 84

The x term is 7.25x.  Take half its coefficient (3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
7.25x + 13.140625 + x2 = 84 + 13.140625

Reorder the terms:
13.140625 + 7.25x + x2 = 84 + 13.140625

Combine like terms: 84 + 13.140625 = 97.140625
13.140625 + 7.25x + x2 = 97.140625

Factor a perfect square on the left side:
(x + 3.625)(x + 3.625) = 97.140625

Calculate the square root of the right side: 9.855994369

Break this problem into two subproblems by setting 
(x + 3.625) equal to 9.855994369 and -9.855994369.


Subproblem 1
x + 3.625 = 9.855994369

Simplifying
x + 3.625 = 9.855994369

Reorder the terms:
3.625 + x = 9.855994369

Solving
3.625 + x = 9.855994369

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = 9.855994369 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = 9.855994369 + -3.625
x = 9.855994369 + -3.625

Combine like terms: 9.855994369 + -3.625 = 6.230994369
x = 6.230994369

Simplifying
x = 6.230994369


Subproblem 2
x + 3.625 = -9.855994369

Simplifying
x + 3.625 = -9.855994369

Reorder the terms:
3.625 + x = -9.855994369

Solving
3.625 + x = -9.855994369

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = -9.855994369 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = -9.855994369 + -3.625
x = -9.855994369 + -3.625

Combine like terms: -9.855994369 + -3.625 = -13.480994369
x = -13.480994369

Simplifying
x = -13.480994369


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.230994369, -13.480994369}

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