x^2+23x+36=0

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Solution for x^2+23x+36=0 equation:


Simplifying
x2 + 23x + 36 = 0

Reorder the terms:
36 + 23x + x2 = 0

Solving
36 + 23x + 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 + 23x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 23x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 23x + x2 = 0 + -36
23x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
23x + x2 = -36

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = -36 + 132.25

Reorder the terms:
132.25 + 23x + x2 = -36 + 132.25

Combine like terms: -36 + 132.25 = 96.25
132.25 + 23x + x2 = 96.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 11.5) equal to 9.810708435 and -9.810708435.

Subproblem 1

x + 11.5 = 9.810708435 Simplifying x + 11.5 = 9.810708435 Reorder the terms: 11.5 + x = 9.810708435 Solving 11.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 9.810708435 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 9.810708435 + -11.5 x = 9.810708435 + -11.5 Combine like terms: 9.810708435 + -11.5 = -1.689291565 x = -1.689291565 Simplifying x = -1.689291565

Subproblem 2

x + 11.5 = -9.810708435 Simplifying x + 11.5 = -9.810708435 Reorder the terms: 11.5 + x = -9.810708435 Solving 11.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -9.810708435 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -9.810708435 + -11.5 x = -9.810708435 + -11.5 Combine like terms: -9.810708435 + -11.5 = -21.310708435 x = -21.310708435 Simplifying x = -21.310708435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.689291565, -21.310708435}

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