x^2+5x-94=0

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Solution for x^2+5x-94=0 equation: 


Simplifying
x2 + 5x + -94 = 0

Reorder the terms:
-94 + 5x + x2 = 0

Solving
-94 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '94' to each side of the equation.
-94 + 5x + 94 + x2 = 0 + 94

Reorder the terms:
-94 + 94 + 5x + x2 = 0 + 94

Combine like terms: -94 + 94 = 0
0 + 5x + x2 = 0 + 94
5x + x2 = 0 + 94

Combine like terms: 0 + 94 = 94
5x + x2 = 94

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 94 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 94 + 6.25

Combine like terms: 94 + 6.25 = 100.25
6.25 + 5x + x2 = 100.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.012492197 and -10.012492197.


Subproblem 1
x + 2.5 = 10.012492197

Simplifying
x + 2.5 = 10.012492197

Reorder the terms:
2.5 + x = 10.012492197

Solving
2.5 + x = 10.012492197

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 10.012492197 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 10.012492197 + -2.5
x = 10.012492197 + -2.5

Combine like terms: 10.012492197 + -2.5 = 7.512492197
x = 7.512492197

Simplifying
x = 7.512492197


Subproblem 2
x + 2.5 = -10.012492197

Simplifying
x + 2.5 = -10.012492197

Reorder the terms:
2.5 + x = -10.012492197

Solving
2.5 + x = -10.012492197

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -10.012492197 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -10.012492197 + -2.5
x = -10.012492197 + -2.5

Combine like terms: -10.012492197 + -2.5 = -12.512492197
x = -12.512492197

Simplifying
x = -12.512492197


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.512492197, -12.512492197}

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