0=x^2-8x-3x-24

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Solution for 0=x^2-8x-3x-24 equation:


Simplifying
0 = x2 + -8x + -3x + -24

Reorder the terms:
0 = -24 + -8x + -3x + x2

Combine like terms: -8x + -3x = -11x
0 = -24 + -11x + x2

Solving
0 = -24 + -11x + x2

Solving for variable 'x'.

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

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

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

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-24 + -11x + x2 = 0

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 = 12.865459931 x = 12.865459931 Simplifying x = 12.865459931

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 = -1.865459931 x = -1.865459931 Simplifying x = -1.865459931

Solution

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

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