X^2+5*X-158=0

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Solution for X^2+5*X-158=0 equation: 


Simplifying
X2 + 5X + -158 = 0

Reorder the terms:
-158 + 5X + X2 = 0

Solving
-158 + 5X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '158' to each side of the equation.
-158 + 5X + 158 + X2 = 0 + 158

Reorder the terms:
-158 + 158 + 5X + X2 = 0 + 158

Combine like terms: -158 + 158 = 0
0 + 5X + X2 = 0 + 158
5X + X2 = 0 + 158

Combine like terms: 0 + 158 = 158
5X + X2 = 158

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 = 158 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 158 + 6.25

Combine like terms: 158 + 6.25 = 164.25
6.25 + 5X + X2 = 164.25

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 164.25

Calculate the square root of the right side: 12.816005618

Break this problem into two subproblems by setting 
(X + 2.5) equal to 12.816005618 and -12.816005618.


Subproblem 1
X + 2.5 = 12.816005618

Simplifying
X + 2.5 = 12.816005618

Reorder the terms:
2.5 + X = 12.816005618

Solving
2.5 + X = 12.816005618

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 = 12.816005618 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 12.816005618 + -2.5
X = 12.816005618 + -2.5

Combine like terms: 12.816005618 + -2.5 = 10.316005618
X = 10.316005618

Simplifying
X = 10.316005618


Subproblem 2
X + 2.5 = -12.816005618

Simplifying
X + 2.5 = -12.816005618

Reorder the terms:
2.5 + X = -12.816005618

Solving
2.5 + X = -12.816005618

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 = -12.816005618 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -12.816005618 + -2.5
X = -12.816005618 + -2.5

Combine like terms: -12.816005618 + -2.5 = -15.316005618
X = -15.316005618

Simplifying
X = -15.316005618


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {10.316005618, -15.316005618}

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