x^2+10x+15x-150=2730

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Solution for x^2+10x+15x-150=2730 equation:


Simplifying
x2 + 10x + 15x + -150 = 2730

Reorder the terms:
-150 + 10x + 15x + x2 = 2730

Combine like terms: 10x + 15x = 25x
-150 + 25x + x2 = 2730

Solving
-150 + 25x + x2 = 2730

Solving for variable 'x'.

Reorder the terms:
-150 + -2730 + 25x + x2 = 2730 + -2730

Combine like terms: -150 + -2730 = -2880
-2880 + 25x + x2 = 2730 + -2730

Combine like terms: 2730 + -2730 = 0
-2880 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2880' to each side of the equation.
-2880 + 25x + 2880 + x2 = 0 + 2880

Reorder the terms:
-2880 + 2880 + 25x + x2 = 0 + 2880

Combine like terms: -2880 + 2880 = 0
0 + 25x + x2 = 0 + 2880
25x + x2 = 0 + 2880

Combine like terms: 0 + 2880 = 2880
25x + x2 = 2880

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 2880 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 2880 + 156.25

Combine like terms: 2880 + 156.25 = 3036.25
156.25 + 25x + x2 = 3036.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 3036.25

Calculate the square root of the right side: 55.102177815

Break this problem into two subproblems by setting 
(x + 12.5) equal to 55.102177815 and -55.102177815.

Subproblem 1

x + 12.5 = 55.102177815 Simplifying x + 12.5 = 55.102177815 Reorder the terms: 12.5 + x = 55.102177815 Solving 12.5 + x = 55.102177815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 55.102177815 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 55.102177815 + -12.5 x = 55.102177815 + -12.5 Combine like terms: 55.102177815 + -12.5 = 42.602177815 x = 42.602177815 Simplifying x = 42.602177815

Subproblem 2

x + 12.5 = -55.102177815 Simplifying x + 12.5 = -55.102177815 Reorder the terms: 12.5 + x = -55.102177815 Solving 12.5 + x = -55.102177815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -55.102177815 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -55.102177815 + -12.5 x = -55.102177815 + -12.5 Combine like terms: -55.102177815 + -12.5 = -67.602177815 x = -67.602177815 Simplifying x = -67.602177815

Solution

The solution to the problem is based on the solutions from the subproblems. x = {42.602177815, -67.602177815}

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