x^2+24x+106=0

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Solution for x^2+24x+106=0 equation:


Simplifying
x2 + 24x + 106 = 0

Reorder the terms:
106 + 24x + x2 = 0

Solving
106 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-106' to each side of the equation.
106 + 24x + -106 + x2 = 0 + -106

Reorder the terms:
106 + -106 + 24x + x2 = 0 + -106

Combine like terms: 106 + -106 = 0
0 + 24x + x2 = 0 + -106
24x + x2 = 0 + -106

Combine like terms: 0 + -106 = -106
24x + x2 = -106

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = -106 + 144

Reorder the terms:
144 + 24x + x2 = -106 + 144

Combine like terms: -106 + 144 = 38
144 + 24x + x2 = 38

Factor a perfect square on the left side:
(x + 12)(x + 12) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + 12) equal to 6.164414003 and -6.164414003.

Subproblem 1

x + 12 = 6.164414003 Simplifying x + 12 = 6.164414003 Reorder the terms: 12 + x = 6.164414003 Solving 12 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 6.164414003 + -12 Combine like terms: 12 + -12 = 0 0 + x = 6.164414003 + -12 x = 6.164414003 + -12 Combine like terms: 6.164414003 + -12 = -5.835585997 x = -5.835585997 Simplifying x = -5.835585997

Subproblem 2

x + 12 = -6.164414003 Simplifying x + 12 = -6.164414003 Reorder the terms: 12 + x = -6.164414003 Solving 12 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -6.164414003 + -12 Combine like terms: 12 + -12 = 0 0 + x = -6.164414003 + -12 x = -6.164414003 + -12 Combine like terms: -6.164414003 + -12 = -18.164414003 x = -18.164414003 Simplifying x = -18.164414003

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.835585997, -18.164414003}

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