x^2+22x=24

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Solution for x^2+22x=24 equation:


Simplifying
x2 + 22x = 24

Reorder the terms:
22x + x2 = 24

Solving
22x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 22x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 22x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 22x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 22x + x2 = 0 + 24
22x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
22x + x2 = 24

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 = 24 + 121

Reorder the terms:
121 + 22x + x2 = 24 + 121

Combine like terms: 24 + 121 = 145
121 + 22x + x2 = 145

Factor a perfect square on the left side:
(x + 11)(x + 11) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + 11) equal to 12.041594579 and -12.041594579.

Subproblem 1

x + 11 = 12.041594579 Simplifying x + 11 = 12.041594579 Reorder the terms: 11 + x = 12.041594579 Solving 11 + x = 12.041594579 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 = 12.041594579 + -11 Combine like terms: 11 + -11 = 0 0 + x = 12.041594579 + -11 x = 12.041594579 + -11 Combine like terms: 12.041594579 + -11 = 1.041594579 x = 1.041594579 Simplifying x = 1.041594579

Subproblem 2

x + 11 = -12.041594579 Simplifying x + 11 = -12.041594579 Reorder the terms: 11 + x = -12.041594579 Solving 11 + x = -12.041594579 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 = -12.041594579 + -11 Combine like terms: 11 + -11 = 0 0 + x = -12.041594579 + -11 x = -12.041594579 + -11 Combine like terms: -12.041594579 + -11 = -23.041594579 x = -23.041594579 Simplifying x = -23.041594579

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.041594579, -23.041594579}

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