x^2+22x=10

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Solution for x^2+22x=10 equation:


Simplifying
x2 + 22x = 10

Reorder the terms:
22x + x2 = 10

Solving
22x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 22x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 22x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 22x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 22x + x2 = 0 + 10
22x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
22x + x2 = 10

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 = 10 + 121

Reorder the terms:
121 + 22x + x2 = 10 + 121

Combine like terms: 10 + 121 = 131
121 + 22x + x2 = 131

Factor a perfect square on the left side:
(x + 11)(x + 11) = 131

Calculate the square root of the right side: 11.445523142

Break this problem into two subproblems by setting 
(x + 11) equal to 11.445523142 and -11.445523142.

Subproblem 1

x + 11 = 11.445523142 Simplifying x + 11 = 11.445523142 Reorder the terms: 11 + x = 11.445523142 Solving 11 + x = 11.445523142 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 = 11.445523142 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.445523142 + -11 x = 11.445523142 + -11 Combine like terms: 11.445523142 + -11 = 0.445523142 x = 0.445523142 Simplifying x = 0.445523142

Subproblem 2

x + 11 = -11.445523142 Simplifying x + 11 = -11.445523142 Reorder the terms: 11 + x = -11.445523142 Solving 11 + x = -11.445523142 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 = -11.445523142 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.445523142 + -11 x = -11.445523142 + -11 Combine like terms: -11.445523142 + -11 = -22.445523142 x = -22.445523142 Simplifying x = -22.445523142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.445523142, -22.445523142}

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