11x=-x^2+24

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Solution for 11x=-x^2+24 equation:


Simplifying
11x = -1x2 + 24

Reorder the terms:
11x = 24 + -1x2

Solving
11x = 24 + -1x2

Solving for variable 'x'.

Reorder the terms:
-24 + 11x + x2 = 24 + -1x2 + -24 + x2

Reorder the terms:
-24 + 11x + x2 = 24 + -24 + -1x2 + x2

Combine like terms: 24 + -24 = 0
-24 + 11x + x2 = 0 + -1x2 + x2
-24 + 11x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-24 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 11x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 11x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 11x + x2 = 0 + 24
11x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
11x + x2 = 24

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 24 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 24 + 30.25

Combine like terms: 24 + 30.25 = 54.25
30.25 + 11x + x2 = 54.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

x + 5.5 = 7.365459931 Simplifying x + 5.5 = 7.365459931 Reorder the terms: 5.5 + x = 7.365459931 Solving 5.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.365459931 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.365459931 + -5.5 x = 7.365459931 + -5.5 Combine like terms: 7.365459931 + -5.5 = 1.865459931 x = 1.865459931 Simplifying x = 1.865459931

Subproblem 2

x + 5.5 = -7.365459931 Simplifying x + 5.5 = -7.365459931 Reorder the terms: 5.5 + x = -7.365459931 Solving 5.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.365459931 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.365459931 + -5.5 x = -7.365459931 + -5.5 Combine like terms: -7.365459931 + -5.5 = -12.865459931 x = -12.865459931 Simplifying x = -12.865459931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.865459931, -12.865459931}

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