x^2+8x=(x+5)(2-8)

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


Simplifying
x2 + 8x = (x + 5)(2 + -8)

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

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

Combine like terms: 2 + -8 = -6
8x + x2 = (5 + x)(-6)

Reorder the terms for easier multiplication:
8x + x2 = -6(5 + x)
8x + x2 = (5 * -6 + x * -6)
8x + x2 = (-30 + -6x)

Solving
8x + x2 = -30 + -6x

Solving for variable 'x'.

Reorder the terms:
30 + 8x + 6x + x2 = -30 + -6x + 30 + 6x

Combine like terms: 8x + 6x = 14x
30 + 14x + x2 = -30 + -6x + 30 + 6x

Reorder the terms:
30 + 14x + x2 = -30 + 30 + -6x + 6x

Combine like terms: -30 + 30 = 0
30 + 14x + x2 = 0 + -6x + 6x
30 + 14x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
30 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 14x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 14x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 14x + x2 = 0 + -30
14x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
14x + x2 = -30

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -30 + 49

Reorder the terms:
49 + 14x + x2 = -30 + 49

Combine like terms: -30 + 49 = 19
49 + 14x + x2 = 19

Factor a perfect square on the left side:
(x + 7)(x + 7) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 7) equal to 4.358898944 and -4.358898944.

Subproblem 1

x + 7 = 4.358898944 Simplifying x + 7 = 4.358898944 Reorder the terms: 7 + x = 4.358898944 Solving 7 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 4.358898944 + -7 Combine like terms: 7 + -7 = 0 0 + x = 4.358898944 + -7 x = 4.358898944 + -7 Combine like terms: 4.358898944 + -7 = -2.641101056 x = -2.641101056 Simplifying x = -2.641101056

Subproblem 2

x + 7 = -4.358898944 Simplifying x + 7 = -4.358898944 Reorder the terms: 7 + x = -4.358898944 Solving 7 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -4.358898944 + -7 Combine like terms: 7 + -7 = 0 0 + x = -4.358898944 + -7 x = -4.358898944 + -7 Combine like terms: -4.358898944 + -7 = -11.358898944 x = -11.358898944 Simplifying x = -11.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.641101056, -11.358898944}

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