(m+8)(m-5)=-8

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Solution for (m+8)(m-5)=-8 equation:


Simplifying
(m + 8)(m + -5) = -8

Reorder the terms:
(8 + m)(m + -5) = -8

Reorder the terms:
(8 + m)(-5 + m) = -8

Multiply (8 + m) * (-5 + m)
(8(-5 + m) + m(-5 + m)) = -8
((-5 * 8 + m * 8) + m(-5 + m)) = -8
((-40 + 8m) + m(-5 + m)) = -8
(-40 + 8m + (-5 * m + m * m)) = -8
(-40 + 8m + (-5m + m2)) = -8

Combine like terms: 8m + -5m = 3m
(-40 + 3m + m2) = -8

Solving
-40 + 3m + m2 = -8

Solving for variable 'm'.

Reorder the terms:
-40 + 8 + 3m + m2 = -8 + 8

Combine like terms: -40 + 8 = -32
-32 + 3m + m2 = -8 + 8

Combine like terms: -8 + 8 = 0
-32 + 3m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 3m + 32 + m2 = 0 + 32

Reorder the terms:
-32 + 32 + 3m + m2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 3m + m2 = 0 + 32
3m + m2 = 0 + 32

Combine like terms: 0 + 32 = 32
3m + m2 = 32

The m term is 3m.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3m + 2.25 + m2 = 32 + 2.25

Reorder the terms:
2.25 + 3m + m2 = 32 + 2.25

Combine like terms: 32 + 2.25 = 34.25
2.25 + 3m + m2 = 34.25

Factor a perfect square on the left side:
(m + 1.5)(m + 1.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(m + 1.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

m + 1.5 = 5.852349955 Simplifying m + 1.5 = 5.852349955 Reorder the terms: 1.5 + m = 5.852349955 Solving 1.5 + m = 5.852349955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 5.852349955 + -1.5 m = 5.852349955 + -1.5 Combine like terms: 5.852349955 + -1.5 = 4.352349955 m = 4.352349955 Simplifying m = 4.352349955

Subproblem 2

m + 1.5 = -5.852349955 Simplifying m + 1.5 = -5.852349955 Reorder the terms: 1.5 + m = -5.852349955 Solving 1.5 + m = -5.852349955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -5.852349955 + -1.5 m = -5.852349955 + -1.5 Combine like terms: -5.852349955 + -1.5 = -7.352349955 m = -7.352349955 Simplifying m = -7.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. m = {4.352349955, -7.352349955}

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