x^2+19x+36=0

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Solution for x^2+19x+36=0 equation:


Simplifying
x2 + 19x + 36 = 0

Reorder the terms:
36 + 19x + x2 = 0

Solving
36 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 19x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 19x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 19x + x2 = 0 + -36
19x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
19x + x2 = -36

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = -36 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -36 + 90.25

Combine like terms: -36 + 90.25 = 54.25
90.25 + 19x + x2 = 54.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + 9.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

x + 9.5 = 7.365459931 Simplifying x + 9.5 = 7.365459931 Reorder the terms: 9.5 + x = 7.365459931 Solving 9.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 7.365459931 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 7.365459931 + -9.5 x = 7.365459931 + -9.5 Combine like terms: 7.365459931 + -9.5 = -2.134540069 x = -2.134540069 Simplifying x = -2.134540069

Subproblem 2

x + 9.5 = -7.365459931 Simplifying x + 9.5 = -7.365459931 Reorder the terms: 9.5 + x = -7.365459931 Solving 9.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -7.365459931 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -7.365459931 + -9.5 x = -7.365459931 + -9.5 Combine like terms: -7.365459931 + -9.5 = -16.865459931 x = -16.865459931 Simplifying x = -16.865459931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.134540069, -16.865459931}

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