x^2+22x+121=24

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Solution for x^2+22x+121=24 equation:


Simplifying
x2 + 22x + 121 = 24

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

Solving
121 + 22x + x2 = 24

Solving for variable 'x'.

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

Combine like terms: 121 + -24 = 97
97 + 22x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
97 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-97' to each side of the equation.
97 + 22x + -97 + x2 = 0 + -97

Reorder the terms:
97 + -97 + 22x + x2 = 0 + -97

Combine like terms: 97 + -97 = 0
0 + 22x + x2 = 0 + -97
22x + x2 = 0 + -97

Combine like terms: 0 + -97 = -97
22x + x2 = -97

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 = -97 + 121

Reorder the terms:
121 + 22x + x2 = -97 + 121

Combine like terms: -97 + 121 = 24
121 + 22x + x2 = 24

Factor a perfect square on the left side:
(x + 11)(x + 11) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 11) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + 11 = 4.898979486 Simplifying x + 11 = 4.898979486 Reorder the terms: 11 + x = 4.898979486 Solving 11 + x = 4.898979486 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 = 4.898979486 + -11 Combine like terms: 11 + -11 = 0 0 + x = 4.898979486 + -11 x = 4.898979486 + -11 Combine like terms: 4.898979486 + -11 = -6.101020514 x = -6.101020514 Simplifying x = -6.101020514

Subproblem 2

x + 11 = -4.898979486 Simplifying x + 11 = -4.898979486 Reorder the terms: 11 + x = -4.898979486 Solving 11 + x = -4.898979486 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 = -4.898979486 + -11 Combine like terms: 11 + -11 = 0 0 + x = -4.898979486 + -11 x = -4.898979486 + -11 Combine like terms: -4.898979486 + -11 = -15.898979486 x = -15.898979486 Simplifying x = -15.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-6.101020514, -15.898979486}

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