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Simplifying m + 6 + -5m2 + 5m = 0 Reorder the terms: 6 + m + 5m + -5m2 = 0 Combine like terms: m + 5m = 6m 6 + 6m + -5m2 = 0 Solving 6 + 6m + -5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + -1.2m + m2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1.2m + 1.2 + m2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1.2m + m2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1.2m + m2 = 0 + 1.2 -1.2m + m2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1.2m + m2 = 1.2 The m term is -1.2m. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2m + 0.36 + m2 = 1.2 + 0.36 Reorder the terms: 0.36 + -1.2m + m2 = 1.2 + 0.36 Combine like terms: 1.2 + 0.36 = 1.56 0.36 + -1.2m + m2 = 1.56 Factor a perfect square on the left side: (m + -0.6)(m + -0.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (m + -0.6) equal to 1.2489996 and -1.2489996.Subproblem 1
m + -0.6 = 1.2489996 Simplifying m + -0.6 = 1.2489996 Reorder the terms: -0.6 + m = 1.2489996 Solving -0.6 + m = 1.2489996 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + m = 1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + m = 1.2489996 + 0.6 m = 1.2489996 + 0.6 Combine like terms: 1.2489996 + 0.6 = 1.8489996 m = 1.8489996 Simplifying m = 1.8489996Subproblem 2
m + -0.6 = -1.2489996 Simplifying m + -0.6 = -1.2489996 Reorder the terms: -0.6 + m = -1.2489996 Solving -0.6 + m = -1.2489996 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + m = -1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + m = -1.2489996 + 0.6 m = -1.2489996 + 0.6 Combine like terms: -1.2489996 + 0.6 = -0.6489996 m = -0.6489996 Simplifying m = -0.6489996Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.8489996, -0.6489996}
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