x^2+7x-10=180

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Solution for x^2+7x-10=180 equation: 


Simplifying
x2 + 7x + -10 = 180

Reorder the terms:
-10 + 7x + x2 = 180

Solving
-10 + 7x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-10 + -180 + 7x + x2 = 180 + -180

Combine like terms: -10 + -180 = -190
-190 + 7x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-190 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '190' to each side of the equation.
-190 + 7x + 190 + x2 = 0 + 190

Reorder the terms:
-190 + 190 + 7x + x2 = 0 + 190

Combine like terms: -190 + 190 = 0
0 + 7x + x2 = 0 + 190
7x + x2 = 0 + 190

Combine like terms: 0 + 190 = 190
7x + x2 = 190

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 = 190 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 190 + 12.25

Combine like terms: 190 + 12.25 = 202.25
12.25 + 7x + x2 = 202.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(x + 3.5) equal to 14.221462653 and -14.221462653.


Subproblem 1
x + 3.5 = 14.221462653

Simplifying
x + 3.5 = 14.221462653

Reorder the terms:
3.5 + x = 14.221462653

Solving
3.5 + x = 14.221462653

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 = 14.221462653 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 14.221462653 + -3.5
x = 14.221462653 + -3.5

Combine like terms: 14.221462653 + -3.5 = 10.721462653
x = 10.721462653

Simplifying
x = 10.721462653


Subproblem 2
x + 3.5 = -14.221462653

Simplifying
x + 3.5 = -14.221462653

Reorder the terms:
3.5 + x = -14.221462653

Solving
3.5 + x = -14.221462653

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 = -14.221462653 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -14.221462653 + -3.5
x = -14.221462653 + -3.5

Combine like terms: -14.221462653 + -3.5 = -17.721462653
x = -17.721462653

Simplifying
x = -17.721462653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.721462653, -17.721462653}

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