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Simplifying 4m2 = -10m + 10 Reorder the terms: 4m2 = 10 + -10m Solving 4m2 = 10 + -10m Solving for variable 'm'. Reorder the terms: -10 + 10m + 4m2 = 10 + -10m + -10 + 10m Reorder the terms: -10 + 10m + 4m2 = 10 + -10 + -10m + 10m Combine like terms: 10 + -10 = 0 -10 + 10m + 4m2 = 0 + -10m + 10m -10 + 10m + 4m2 = -10m + 10m Combine like terms: -10m + 10m = 0 -10 + 10m + 4m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 5m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 5m + 2m2)' equal to zero and attempt to solve: Simplifying -5 + 5m + 2m2 = 0 Solving -5 + 5m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 2.5m + m2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.5m + 2.5 + m2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.5m + m2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.5m + m2 = 0 + 2.5 2.5m + m2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.5m + m2 = 2.5 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 = 2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 2.5 + 1.5625 Combine like terms: 2.5 + 1.5625 = 4.0625 1.5625 + 2.5m + m2 = 4.0625 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (m + 1.25) equal to 2.015564437 and -2.015564437.Subproblem 1
m + 1.25 = 2.015564437 Simplifying m + 1.25 = 2.015564437 Reorder the terms: 1.25 + m = 2.015564437 Solving 1.25 + m = 2.015564437 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 = 2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 2.015564437 + -1.25 m = 2.015564437 + -1.25 Combine like terms: 2.015564437 + -1.25 = 0.765564437 m = 0.765564437 Simplifying m = 0.765564437Subproblem 2
m + 1.25 = -2.015564437 Simplifying m + 1.25 = -2.015564437 Reorder the terms: 1.25 + m = -2.015564437 Solving 1.25 + m = -2.015564437 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 = -2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -2.015564437 + -1.25 m = -2.015564437 + -1.25 Combine like terms: -2.015564437 + -1.25 = -3.265564437 m = -3.265564437 Simplifying m = -3.265564437Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.765564437, -3.265564437}Solution
m = {0.765564437, -3.265564437}
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