x^2=22x+42

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Solution for x^2=22x+42 equation:


Simplifying
x2 = 22x + 42

Reorder the terms:
x2 = 42 + 22x

Solving
x2 = 42 + 22x

Solving for variable 'x'.

Reorder the terms:
-42 + -22x + x2 = 42 + 22x + -42 + -22x

Reorder the terms:
-42 + -22x + x2 = 42 + -42 + 22x + -22x

Combine like terms: 42 + -42 = 0
-42 + -22x + x2 = 0 + 22x + -22x
-42 + -22x + x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
-42 + -22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -22x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + -22x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -22x + x2 = 0 + 42
-22x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
-22x + x2 = 42

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 = 42 + 121

Reorder the terms:
121 + -22x + x2 = 42 + 121

Combine like terms: 42 + 121 = 163
121 + -22x + x2 = 163

Factor a perfect square on the left side:
(x + -11)(x + -11) = 163

Calculate the square root of the right side: 12.767145335

Break this problem into two subproblems by setting 
(x + -11) equal to 12.767145335 and -12.767145335.

Subproblem 1

x + -11 = 12.767145335 Simplifying x + -11 = 12.767145335 Reorder the terms: -11 + x = 12.767145335 Solving -11 + x = 12.767145335 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 = 12.767145335 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.767145335 + 11 x = 12.767145335 + 11 Combine like terms: 12.767145335 + 11 = 23.767145335 x = 23.767145335 Simplifying x = 23.767145335

Subproblem 2

x + -11 = -12.767145335 Simplifying x + -11 = -12.767145335 Reorder the terms: -11 + x = -12.767145335 Solving -11 + x = -12.767145335 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 = -12.767145335 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.767145335 + 11 x = -12.767145335 + 11 Combine like terms: -12.767145335 + 11 = -1.767145335 x = -1.767145335 Simplifying x = -1.767145335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.767145335, -1.767145335}

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