x^2+10x+24=119

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Solution for x^2+10x+24=119 equation:


Simplifying
x2 + 10x + 24 = 119

Reorder the terms:
24 + 10x + x2 = 119

Solving
24 + 10x + x2 = 119

Solving for variable 'x'.

Reorder the terms:
24 + -119 + 10x + x2 = 119 + -119

Combine like terms: 24 + -119 = -95
-95 + 10x + x2 = 119 + -119

Combine like terms: 119 + -119 = 0
-95 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '95' to each side of the equation.
-95 + 10x + 95 + x2 = 0 + 95

Reorder the terms:
-95 + 95 + 10x + x2 = 0 + 95

Combine like terms: -95 + 95 = 0
0 + 10x + x2 = 0 + 95
10x + x2 = 0 + 95

Combine like terms: 0 + 95 = 95
10x + x2 = 95

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 = 95 + 25

Reorder the terms:
25 + 10x + x2 = 95 + 25

Combine like terms: 95 + 25 = 120
25 + 10x + x2 = 120

Factor a perfect square on the left side:
(x + 5)(x + 5) = 120

Calculate the square root of the right side: 10.95445115

Break this problem into two subproblems by setting 
(x + 5) equal to 10.95445115 and -10.95445115.

Subproblem 1

x + 5 = 10.95445115 Simplifying x + 5 = 10.95445115 Reorder the terms: 5 + x = 10.95445115 Solving 5 + x = 10.95445115 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 = 10.95445115 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.95445115 + -5 x = 10.95445115 + -5 Combine like terms: 10.95445115 + -5 = 5.95445115 x = 5.95445115 Simplifying x = 5.95445115

Subproblem 2

x + 5 = -10.95445115 Simplifying x + 5 = -10.95445115 Reorder the terms: 5 + x = -10.95445115 Solving 5 + x = -10.95445115 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 = -10.95445115 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.95445115 + -5 x = -10.95445115 + -5 Combine like terms: -10.95445115 + -5 = -15.95445115 x = -15.95445115 Simplifying x = -15.95445115

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.95445115, -15.95445115}

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