x^2+36x-35=115

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Solution for x^2+36x-35=115 equation:


Simplifying
x2 + 36x + -35 = 115

Reorder the terms:
-35 + 36x + x2 = 115

Solving
-35 + 36x + x2 = 115

Solving for variable 'x'.

Reorder the terms:
-35 + -115 + 36x + x2 = 115 + -115

Combine like terms: -35 + -115 = -150
-150 + 36x + x2 = 115 + -115

Combine like terms: 115 + -115 = 0
-150 + 36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + 36x + 150 + x2 = 0 + 150

Reorder the terms:
-150 + 150 + 36x + x2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 36x + x2 = 0 + 150
36x + x2 = 0 + 150

Combine like terms: 0 + 150 = 150
36x + x2 = 150

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = 150 + 324

Reorder the terms:
324 + 36x + x2 = 150 + 324

Combine like terms: 150 + 324 = 474
324 + 36x + x2 = 474

Factor a perfect square on the left side:
(x + 18)(x + 18) = 474

Calculate the square root of the right side: 21.771541057

Break this problem into two subproblems by setting 
(x + 18) equal to 21.771541057 and -21.771541057.

Subproblem 1

x + 18 = 21.771541057 Simplifying x + 18 = 21.771541057 Reorder the terms: 18 + x = 21.771541057 Solving 18 + x = 21.771541057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 21.771541057 + -18 Combine like terms: 18 + -18 = 0 0 + x = 21.771541057 + -18 x = 21.771541057 + -18 Combine like terms: 21.771541057 + -18 = 3.771541057 x = 3.771541057 Simplifying x = 3.771541057

Subproblem 2

x + 18 = -21.771541057 Simplifying x + 18 = -21.771541057 Reorder the terms: 18 + x = -21.771541057 Solving 18 + x = -21.771541057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -21.771541057 + -18 Combine like terms: 18 + -18 = 0 0 + x = -21.771541057 + -18 x = -21.771541057 + -18 Combine like terms: -21.771541057 + -18 = -39.771541057 x = -39.771541057 Simplifying x = -39.771541057

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.771541057, -39.771541057}

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