x^2+4x-52=180

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Solution for x^2+4x-52=180 equation:


Simplifying
x2 + 4x + -52 = 180

Reorder the terms:
-52 + 4x + x2 = 180

Solving
-52 + 4x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-52 + -180 + 4x + x2 = 180 + -180

Combine like terms: -52 + -180 = -232
-232 + 4x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-232 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '232' to each side of the equation.
-232 + 4x + 232 + x2 = 0 + 232

Reorder the terms:
-232 + 232 + 4x + x2 = 0 + 232

Combine like terms: -232 + 232 = 0
0 + 4x + x2 = 0 + 232
4x + x2 = 0 + 232

Combine like terms: 0 + 232 = 232
4x + x2 = 232

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 232 + 4

Reorder the terms:
4 + 4x + x2 = 232 + 4

Combine like terms: 232 + 4 = 236
4 + 4x + x2 = 236

Factor a perfect square on the left side:
(x + 2)(x + 2) = 236

Calculate the square root of the right side: 15.362291496

Break this problem into two subproblems by setting 
(x + 2) equal to 15.362291496 and -15.362291496.

Subproblem 1

x + 2 = 15.362291496 Simplifying x + 2 = 15.362291496 Reorder the terms: 2 + x = 15.362291496 Solving 2 + x = 15.362291496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 15.362291496 + -2 Combine like terms: 2 + -2 = 0 0 + x = 15.362291496 + -2 x = 15.362291496 + -2 Combine like terms: 15.362291496 + -2 = 13.362291496 x = 13.362291496 Simplifying x = 13.362291496

Subproblem 2

x + 2 = -15.362291496 Simplifying x + 2 = -15.362291496 Reorder the terms: 2 + x = -15.362291496 Solving 2 + x = -15.362291496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -15.362291496 + -2 Combine like terms: 2 + -2 = 0 0 + x = -15.362291496 + -2 x = -15.362291496 + -2 Combine like terms: -15.362291496 + -2 = -17.362291496 x = -17.362291496 Simplifying x = -17.362291496

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.362291496, -17.362291496}

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