1x(x-8)+2(x-8)=x-3

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Solution for 1x(x-8)+2(x-8)=x-3 equation:


Simplifying
1x(x + -8) + 2(x + -8) = x + -3

Reorder the terms:
1x(-8 + x) + 2(x + -8) = x + -3
(-8 * 1x + x * 1x) + 2(x + -8) = x + -3
(-8x + 1x2) + 2(x + -8) = x + -3

Reorder the terms:
-8x + 1x2 + 2(-8 + x) = x + -3
-8x + 1x2 + (-8 * 2 + x * 2) = x + -3
-8x + 1x2 + (-16 + 2x) = x + -3

Reorder the terms:
-16 + -8x + 2x + 1x2 = x + -3

Combine like terms: -8x + 2x = -6x
-16 + -6x + 1x2 = x + -3

Reorder the terms:
-16 + -6x + 1x2 = -3 + x

Solving
-16 + -6x + 1x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
-16 + 3 + -6x + -1x + 1x2 = -3 + x + 3 + -1x

Combine like terms: -16 + 3 = -13
-13 + -6x + -1x + 1x2 = -3 + x + 3 + -1x

Combine like terms: -6x + -1x = -7x
-13 + -7x + 1x2 = -3 + x + 3 + -1x

Reorder the terms:
-13 + -7x + 1x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
-13 + -7x + 1x2 = 0 + x + -1x
-13 + -7x + 1x2 = x + -1x

Combine like terms: x + -1x = 0
-13 + -7x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -7x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -7x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -7x + x2 = 0 + 13
-7x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-7x + x2 = 13

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 13 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 13 + 12.25

Combine like terms: 13 + 12.25 = 25.25
12.25 + -7x + x2 = 25.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.024937811 and -5.024937811.

Subproblem 1

x + -3.5 = 5.024937811 Simplifying x + -3.5 = 5.024937811 Reorder the terms: -3.5 + x = 5.024937811 Solving -3.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.024937811 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.024937811 + 3.5 x = 5.024937811 + 3.5 Combine like terms: 5.024937811 + 3.5 = 8.524937811 x = 8.524937811 Simplifying x = 8.524937811

Subproblem 2

x + -3.5 = -5.024937811 Simplifying x + -3.5 = -5.024937811 Reorder the terms: -3.5 + x = -5.024937811 Solving -3.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.024937811 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.024937811 + 3.5 x = -5.024937811 + 3.5 Combine like terms: -5.024937811 + 3.5 = -1.524937811 x = -1.524937811 Simplifying x = -1.524937811

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.524937811, -1.524937811}

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