15x-x^2=5

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Solution for 15x-x^2=5 equation:


Simplifying
15x + -1x2 = 5

Solving
15x + -1x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 15x + -1x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 15x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -15x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -15x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -15x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -15x + x2 = 0 + -5
-15x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-15x + x2 = -5

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 = -5 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -5 + 56.25

Combine like terms: -5 + 56.25 = 51.25
56.25 + -15x + x2 = 51.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(x + -7.5) equal to 7.158910532 and -7.158910532.

Subproblem 1

x + -7.5 = 7.158910532 Simplifying x + -7.5 = 7.158910532 Reorder the terms: -7.5 + x = 7.158910532 Solving -7.5 + x = 7.158910532 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 = 7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.158910532 + 7.5 x = 7.158910532 + 7.5 Combine like terms: 7.158910532 + 7.5 = 14.658910532 x = 14.658910532 Simplifying x = 14.658910532

Subproblem 2

x + -7.5 = -7.158910532 Simplifying x + -7.5 = -7.158910532 Reorder the terms: -7.5 + x = -7.158910532 Solving -7.5 + x = -7.158910532 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 = -7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.158910532 + 7.5 x = -7.158910532 + 7.5 Combine like terms: -7.158910532 + 7.5 = 0.341089468 x = 0.341089468 Simplifying x = 0.341089468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.658910532, 0.341089468}

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