x^2=22x+15

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Solution for x^2=22x+15 equation:


Simplifying
x2 = 22x + 15

Reorder the terms:
x2 = 15 + 22x

Solving
x2 = 15 + 22x

Solving for variable 'x'.

Reorder the terms:
-15 + -22x + x2 = 15 + 22x + -15 + -22x

Reorder the terms:
-15 + -22x + x2 = 15 + -15 + 22x + -22x

Combine like terms: 15 + -15 = 0
-15 + -22x + x2 = 0 + 22x + -22x
-15 + -22x + x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
-15 + -22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -22x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -22x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -22x + x2 = 0 + 15
-22x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-22x + x2 = 15

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 15 + 121

Reorder the terms:
121 + -22x + x2 = 15 + 121

Combine like terms: 15 + 121 = 136
121 + -22x + x2 = 136

Factor a perfect square on the left side:
(x + -11)(x + -11) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x + -11) equal to 11.66190379 and -11.66190379.

Subproblem 1

x + -11 = 11.66190379 Simplifying x + -11 = 11.66190379 Reorder the terms: -11 + x = 11.66190379 Solving -11 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 11.66190379 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.66190379 + 11 x = 11.66190379 + 11 Combine like terms: 11.66190379 + 11 = 22.66190379 x = 22.66190379 Simplifying x = 22.66190379

Subproblem 2

x + -11 = -11.66190379 Simplifying x + -11 = -11.66190379 Reorder the terms: -11 + x = -11.66190379 Solving -11 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -11.66190379 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.66190379 + 11 x = -11.66190379 + 11 Combine like terms: -11.66190379 + 11 = -0.66190379 x = -0.66190379 Simplifying x = -0.66190379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.66190379, -0.66190379}

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