x^2-5x-8=2+3x

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Solution for x^2-5x-8=2+3x equation:


Simplifying
x2 + -5x + -8 = 2 + 3x

Reorder the terms:
-8 + -5x + x2 = 2 + 3x

Solving
-8 + -5x + x2 = 2 + 3x

Solving for variable 'x'.

Reorder the terms:
-8 + -2 + -5x + -3x + x2 = 2 + 3x + -2 + -3x

Combine like terms: -8 + -2 = -10
-10 + -5x + -3x + x2 = 2 + 3x + -2 + -3x

Combine like terms: -5x + -3x = -8x
-10 + -8x + x2 = 2 + 3x + -2 + -3x

Reorder the terms:
-10 + -8x + x2 = 2 + -2 + 3x + -3x

Combine like terms: 2 + -2 = 0
-10 + -8x + x2 = 0 + 3x + -3x
-10 + -8x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -8x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -8x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -8x + x2 = 0 + 10
-8x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-8x + x2 = 10

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 10 + 16

Reorder the terms:
16 + -8x + x2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + -8x + x2 = 26

Factor a perfect square on the left side:
(x + -4)(x + -4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + -4) equal to 5.099019514 and -5.099019514.

Subproblem 1

x + -4 = 5.099019514 Simplifying x + -4 = 5.099019514 Reorder the terms: -4 + x = 5.099019514 Solving -4 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.099019514 + 4 x = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 x = 9.099019514 Simplifying x = 9.099019514

Subproblem 2

x + -4 = -5.099019514 Simplifying x + -4 = -5.099019514 Reorder the terms: -4 + x = -5.099019514 Solving -4 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.099019514 + 4 x = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 x = -1.099019514 Simplifying x = -1.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.099019514, -1.099019514}

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