x^2+7x+13=180

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Solution for x^2+7x+13=180 equation:


Simplifying
x2 + 7x + 13 = 180

Reorder the terms:
13 + 7x + x2 = 180

Solving
13 + 7x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
13 + -180 + 7x + x2 = 180 + -180

Combine like terms: 13 + -180 = -167
-167 + 7x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-167 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '167' to each side of the equation.
-167 + 7x + 167 + x2 = 0 + 167

Reorder the terms:
-167 + 167 + 7x + x2 = 0 + 167

Combine like terms: -167 + 167 = 0
0 + 7x + x2 = 0 + 167
7x + x2 = 0 + 167

Combine like terms: 0 + 167 = 167
7x + x2 = 167

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 167 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 167 + 12.25

Combine like terms: 167 + 12.25 = 179.25
12.25 + 7x + x2 = 179.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 179.25

Calculate the square root of the right side: 13.388427839

Break this problem into two subproblems by setting 
(x + 3.5) equal to 13.388427839 and -13.388427839.

Subproblem 1

x + 3.5 = 13.388427839 Simplifying x + 3.5 = 13.388427839 Reorder the terms: 3.5 + x = 13.388427839 Solving 3.5 + x = 13.388427839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 13.388427839 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 13.388427839 + -3.5 x = 13.388427839 + -3.5 Combine like terms: 13.388427839 + -3.5 = 9.888427839 x = 9.888427839 Simplifying x = 9.888427839

Subproblem 2

x + 3.5 = -13.388427839 Simplifying x + 3.5 = -13.388427839 Reorder the terms: 3.5 + x = -13.388427839 Solving 3.5 + x = -13.388427839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -13.388427839 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -13.388427839 + -3.5 x = -13.388427839 + -3.5 Combine like terms: -13.388427839 + -3.5 = -16.888427839 x = -16.888427839 Simplifying x = -16.888427839

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.888427839, -16.888427839}

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