X^2+10X-112=0

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Solution for X^2+10X-112=0 equation:


Simplifying
X2 + 10X + -112 = 0

Reorder the terms:
-112 + 10X + X2 = 0

Solving
-112 + 10X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + 10X + 112 + X2 = 0 + 112

Reorder the terms:
-112 + 112 + 10X + X2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + 10X + X2 = 0 + 112
10X + X2 = 0 + 112

Combine like terms: 0 + 112 = 112
10X + X2 = 112

The X term is 10X.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10X + 25 + X2 = 112 + 25

Reorder the terms:
25 + 10X + X2 = 112 + 25

Combine like terms: 112 + 25 = 137
25 + 10X + X2 = 137

Factor a perfect square on the left side:
(X + 5)(X + 5) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(X + 5) equal to 11.704699911 and -11.704699911.

Subproblem 1

X + 5 = 11.704699911 Simplifying X + 5 = 11.704699911 Reorder the terms: 5 + X = 11.704699911 Solving 5 + X = 11.704699911 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = 11.704699911 + -5 Combine like terms: 5 + -5 = 0 0 + X = 11.704699911 + -5 X = 11.704699911 + -5 Combine like terms: 11.704699911 + -5 = 6.704699911 X = 6.704699911 Simplifying X = 6.704699911

Subproblem 2

X + 5 = -11.704699911 Simplifying X + 5 = -11.704699911 Reorder the terms: 5 + X = -11.704699911 Solving 5 + X = -11.704699911 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = -11.704699911 + -5 Combine like terms: 5 + -5 = 0 0 + X = -11.704699911 + -5 X = -11.704699911 + -5 Combine like terms: -11.704699911 + -5 = -16.704699911 X = -16.704699911 Simplifying X = -16.704699911

Solution

The solution to the problem is based on the solutions from the subproblems. X = {6.704699911, -16.704699911}

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