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Simplifying 10m2 + -4m = 142 Reorder the terms: -4m + 10m2 = 142 Solving -4m + 10m2 = 142 Solving for variable 'm'. Reorder the terms: -142 + -4m + 10m2 = 142 + -142 Combine like terms: 142 + -142 = 0 -142 + -4m + 10m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-71 + -2m + 5m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-71 + -2m + 5m2)' equal to zero and attempt to solve: Simplifying -71 + -2m + 5m2 = 0 Solving -71 + -2m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.2 + -0.4m + m2 = 0 Move the constant term to the right: Add '14.2' to each side of the equation. -14.2 + -0.4m + 14.2 + m2 = 0 + 14.2 Reorder the terms: -14.2 + 14.2 + -0.4m + m2 = 0 + 14.2 Combine like terms: -14.2 + 14.2 = 0.0 0.0 + -0.4m + m2 = 0 + 14.2 -0.4m + m2 = 0 + 14.2 Combine like terms: 0 + 14.2 = 14.2 -0.4m + m2 = 14.2 The m term is -0.4m. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4m + 0.04 + m2 = 14.2 + 0.04 Reorder the terms: 0.04 + -0.4m + m2 = 14.2 + 0.04 Combine like terms: 14.2 + 0.04 = 14.24 0.04 + -0.4m + m2 = 14.24 Factor a perfect square on the left side: (m + -0.2)(m + -0.2) = 14.24 Calculate the square root of the right side: 3.773592453 Break this problem into two subproblems by setting (m + -0.2) equal to 3.773592453 and -3.773592453.Subproblem 1
m + -0.2 = 3.773592453 Simplifying m + -0.2 = 3.773592453 Reorder the terms: -0.2 + m = 3.773592453 Solving -0.2 + m = 3.773592453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = 3.773592453 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = 3.773592453 + 0.2 m = 3.773592453 + 0.2 Combine like terms: 3.773592453 + 0.2 = 3.973592453 m = 3.973592453 Simplifying m = 3.973592453Subproblem 2
m + -0.2 = -3.773592453 Simplifying m + -0.2 = -3.773592453 Reorder the terms: -0.2 + m = -3.773592453 Solving -0.2 + m = -3.773592453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = -3.773592453 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = -3.773592453 + 0.2 m = -3.773592453 + 0.2 Combine like terms: -3.773592453 + 0.2 = -3.573592453 m = -3.573592453 Simplifying m = -3.573592453Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.973592453, -3.573592453}Solution
m = {3.973592453, -3.573592453}
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