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Simplifying 4m2 + -12 = -10m Reorder the terms: -12 + 4m2 = -10m Solving -12 + 4m2 = -10m Solving for variable 'm'. Reorder the terms: -12 + 10m + 4m2 = -10m + 10m Combine like terms: -10m + 10m = 0 -12 + 10m + 4m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 5m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 5m + 2m2)' equal to zero and attempt to solve: Simplifying -6 + 5m + 2m2 = 0 Solving -6 + 5m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 2.5m + m2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.5m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + 2.5m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.5m + m2 = 0 + 3 2.5m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.5m + m2 = 3 The m term is 2.5m. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5m + 1.5625 + m2 = 3 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + 2.5m + m2 = 4.5625 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (m + 1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
m + 1.25 = 2.136000936 Simplifying m + 1.25 = 2.136000936 Reorder the terms: 1.25 + m = 2.136000936 Solving 1.25 + m = 2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = 2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 2.136000936 + -1.25 m = 2.136000936 + -1.25 Combine like terms: 2.136000936 + -1.25 = 0.886000936 m = 0.886000936 Simplifying m = 0.886000936Subproblem 2
m + 1.25 = -2.136000936 Simplifying m + 1.25 = -2.136000936 Reorder the terms: 1.25 + m = -2.136000936 Solving 1.25 + m = -2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = -2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -2.136000936 + -1.25 m = -2.136000936 + -1.25 Combine like terms: -2.136000936 + -1.25 = -3.386000936 m = -3.386000936 Simplifying m = -3.386000936Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.886000936, -3.386000936}Solution
m = {0.886000936, -3.386000936}
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