x^2-15x=15

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Solution for x^2-15x=15 equation:


Simplifying
x2 + -15x = 15

Reorder the terms:
-15x + x2 = 15

Solving
-15x + x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -15x + x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -15x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -15x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -15x + x2 = 0 + 15
-15x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-15x + x2 = 15

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 15 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 15 + 56.25

Combine like terms: 15 + 56.25 = 71.25
56.25 + -15x + x2 = 71.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 71.25

Calculate the square root of the right side: 8.440971508

Break this problem into two subproblems by setting 
(x + -7.5) equal to 8.440971508 and -8.440971508.

Subproblem 1

x + -7.5 = 8.440971508 Simplifying x + -7.5 = 8.440971508 Reorder the terms: -7.5 + x = 8.440971508 Solving -7.5 + x = 8.440971508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.440971508 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.440971508 + 7.5 x = 8.440971508 + 7.5 Combine like terms: 8.440971508 + 7.5 = 15.940971508 x = 15.940971508 Simplifying x = 15.940971508

Subproblem 2

x + -7.5 = -8.440971508 Simplifying x + -7.5 = -8.440971508 Reorder the terms: -7.5 + x = -8.440971508 Solving -7.5 + x = -8.440971508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.440971508 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.440971508 + 7.5 x = -8.440971508 + 7.5 Combine like terms: -8.440971508 + 7.5 = -0.940971508 x = -0.940971508 Simplifying x = -0.940971508

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.940971508, -0.940971508}

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