x^2+24x+19=

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Solution for x^2+24x+19= equation:


Simplifying
x2 + 24x + 19 = 0

Reorder the terms:
19 + 24x + x2 = 0

Solving
19 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 24x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 24x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 24x + x2 = 0 + -19
24x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
24x + x2 = -19

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 = -19 + 144

Reorder the terms:
144 + 24x + x2 = -19 + 144

Combine like terms: -19 + 144 = 125
144 + 24x + x2 = 125

Factor a perfect square on the left side:
(x + 12)(x + 12) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + 12) equal to 11.180339887 and -11.180339887.

Subproblem 1

x + 12 = 11.180339887 Simplifying x + 12 = 11.180339887 Reorder the terms: 12 + x = 11.180339887 Solving 12 + x = 11.180339887 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 = 11.180339887 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.180339887 + -12 x = 11.180339887 + -12 Combine like terms: 11.180339887 + -12 = -0.819660113 x = -0.819660113 Simplifying x = -0.819660113

Subproblem 2

x + 12 = -11.180339887 Simplifying x + 12 = -11.180339887 Reorder the terms: 12 + x = -11.180339887 Solving 12 + x = -11.180339887 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 = -11.180339887 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.180339887 + -12 x = -11.180339887 + -12 Combine like terms: -11.180339887 + -12 = -23.180339887 x = -23.180339887 Simplifying x = -23.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.819660113, -23.180339887}

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