2m(m+10)=180

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Solution for 2m(m+10)=180 equation:


Simplifying
2m(m + 10) = 180

Reorder the terms:
2m(10 + m) = 180
(10 * 2m + m * 2m) = 180
(20m + 2m2) = 180

Solving
20m + 2m2 = 180

Solving for variable 'm'.

Reorder the terms:
-180 + 20m + 2m2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 20m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 10m + m2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-90 + 10m + m2)' equal to zero and attempt to solve: Simplifying -90 + 10m + m2 = 0 Solving -90 + 10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 10m + 90 + m2 = 0 + 90 Reorder the terms: -90 + 90 + 10m + m2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 10m + m2 = 0 + 90 10m + m2 = 0 + 90 Combine like terms: 0 + 90 = 90 10m + m2 = 90 The m term is 10m. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10m + 25 + m2 = 90 + 25 Reorder the terms: 25 + 10m + m2 = 90 + 25 Combine like terms: 90 + 25 = 115 25 + 10m + m2 = 115 Factor a perfect square on the left side: (m + 5)(m + 5) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (m + 5) equal to 10.723805295 and -10.723805295.

Subproblem 1

m + 5 = 10.723805295 Simplifying m + 5 = 10.723805295 Reorder the terms: 5 + m = 10.723805295 Solving 5 + m = 10.723805295 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = 10.723805295 + -5 Combine like terms: 5 + -5 = 0 0 + m = 10.723805295 + -5 m = 10.723805295 + -5 Combine like terms: 10.723805295 + -5 = 5.723805295 m = 5.723805295 Simplifying m = 5.723805295

Subproblem 2

m + 5 = -10.723805295 Simplifying m + 5 = -10.723805295 Reorder the terms: 5 + m = -10.723805295 Solving 5 + m = -10.723805295 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = -10.723805295 + -5 Combine like terms: 5 + -5 = 0 0 + m = -10.723805295 + -5 m = -10.723805295 + -5 Combine like terms: -10.723805295 + -5 = -15.723805295 m = -15.723805295 Simplifying m = -15.723805295

Solution

The solution to the problem is based on the solutions from the subproblems. m = {5.723805295, -15.723805295}

Solution

m = {5.723805295, -15.723805295}

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