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 = 5x
-150 + 5x + x2 = 2730

Solving
-150 + 5x + x2 = 2730

Solving for variable 'x'.

Reorder the terms:
-150 + -2730 + 5x + x2 = 2730 + -2730

Combine like terms: -150 + -2730 = -2880
-2880 + 5x + x2 = 2730 + -2730

Combine like terms: 2730 + -2730 = 0
-2880 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2880' to each side of the equation.
-2880 + 5x + 2880 + x2 = 0 + 2880

Reorder the terms:
-2880 + 2880 + 5x + x2 = 0 + 2880

Combine like terms: -2880 + 2880 = 0
0 + 5x + x2 = 0 + 2880
5x + x2 = 0 + 2880

Combine like terms: 0 + 2880 = 2880
5x + x2 = 2880

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2880 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2880 + 6.25

Combine like terms: 2880 + 6.25 = 2886.25
6.25 + 5x + x2 = 2886.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 2886.25

Calculate the square root of the right side: 53.723830839

Break this problem into two subproblems by setting 
(x + 2.5) equal to 53.723830839 and -53.723830839.

Subproblem 1

x + 2.5 = 53.723830839 Simplifying x + 2.5 = 53.723830839 Reorder the terms: 2.5 + x = 53.723830839 Solving 2.5 + x = 53.723830839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 53.723830839 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 53.723830839 + -2.5 x = 53.723830839 + -2.5 Combine like terms: 53.723830839 + -2.5 = 51.223830839 x = 51.223830839 Simplifying x = 51.223830839

Subproblem 2

x + 2.5 = -53.723830839 Simplifying x + 2.5 = -53.723830839 Reorder the terms: 2.5 + x = -53.723830839 Solving 2.5 + x = -53.723830839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -53.723830839 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -53.723830839 + -2.5 x = -53.723830839 + -2.5 Combine like terms: -53.723830839 + -2.5 = -56.223830839 x = -56.223830839 Simplifying x = -56.223830839

Solution

The solution to the problem is based on the solutions from the subproblems. x = {51.223830839, -56.223830839}

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