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Simplifying 12m2 + -36m = 36 Reorder the terms: -36m + 12m2 = 36 Solving -36m + 12m2 = 36 Solving for variable 'm'. Reorder the terms: -36 + -36m + 12m2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -36m + 12m2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-3 + -3m + m2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-3 + -3m + m2)' equal to zero and attempt to solve: Simplifying -3 + -3m + m2 = 0 Solving -3 + -3m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -3m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + -3m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3m + m2 = 0 + 3 -3m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3m + m2 = 3 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 = 3 + 2.25 Reorder the terms: 2.25 + -3m + m2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3m + m2 = 5.25 Factor a perfect square on the left side: (m + -1.5)(m + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (m + -1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
m + -1.5 = 2.291287847 Simplifying m + -1.5 = 2.291287847 Reorder the terms: -1.5 + m = 2.291287847 Solving -1.5 + m = 2.291287847 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 = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = 2.291287847 + 1.5 m = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 m = 3.791287847 Simplifying m = 3.791287847Subproblem 2
m + -1.5 = -2.291287847 Simplifying m + -1.5 = -2.291287847 Reorder the terms: -1.5 + m = -2.291287847 Solving -1.5 + m = -2.291287847 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 = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = -2.291287847 + 1.5 m = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 m = -0.791287847 Simplifying m = -0.791287847Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.791287847, -0.791287847}Solution
m = {3.791287847, -0.791287847}
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