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Simplifying -2m(m + -7) = 4m + -4 Reorder the terms: -2m(-7 + m) = 4m + -4 (-7 * -2m + m * -2m) = 4m + -4 (14m + -2m2) = 4m + -4 Reorder the terms: 14m + -2m2 = -4 + 4m Solving 14m + -2m2 = -4 + 4m Solving for variable 'm'. Reorder the terms: 4 + 14m + -4m + -2m2 = -4 + 4m + 4 + -4m Combine like terms: 14m + -4m = 10m 4 + 10m + -2m2 = -4 + 4m + 4 + -4m Reorder the terms: 4 + 10m + -2m2 = -4 + 4 + 4m + -4m Combine like terms: -4 + 4 = 0 4 + 10m + -2m2 = 0 + 4m + -4m 4 + 10m + -2m2 = 4m + -4m Combine like terms: 4m + -4m = 0 4 + 10m + -2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 5m + -1m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 5m + -1m2)' equal to zero and attempt to solve: Simplifying 2 + 5m + -1m2 = 0 Solving 2 + 5m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -5m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -5m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + -5m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5m + m2 = 0 + 2 -5m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5m + m2 = 2 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = 2 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5m + m2 = 8.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (m + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
m + -2.5 = 2.872281323 Simplifying m + -2.5 = 2.872281323 Reorder the terms: -2.5 + m = 2.872281323 Solving -2.5 + m = 2.872281323 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 2.872281323 + 2.5 m = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 m = 5.372281323 Simplifying m = 5.372281323Subproblem 2
m + -2.5 = -2.872281323 Simplifying m + -2.5 = -2.872281323 Reorder the terms: -2.5 + m = -2.872281323 Solving -2.5 + m = -2.872281323 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -2.872281323 + 2.5 m = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 m = -0.372281323 Simplifying m = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.372281323, -0.372281323}Solution
m = {5.372281323, -0.372281323}
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