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Simplifying 5m2 + 3m = 7 Reorder the terms: 3m + 5m2 = 7 Solving 3m + 5m2 = 7 Solving for variable 'm'. Reorder the terms: -7 + 3m + 5m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 3m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 0.6m + m2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 0.6m + 1.4 + m2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 0.6m + m2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 0.6m + m2 = 0 + 1.4 0.6m + m2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 0.6m + m2 = 1.4 The m term is 0.6m. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6m + 0.09 + m2 = 1.4 + 0.09 Reorder the terms: 0.09 + 0.6m + m2 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + 0.6m + m2 = 1.49 Factor a perfect square on the left side: (m + 0.3)(m + 0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (m + 0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
m + 0.3 = 1.220655562 Simplifying m + 0.3 = 1.220655562 Reorder the terms: 0.3 + m = 1.220655562 Solving 0.3 + m = 1.220655562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + m = 1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + m = 1.220655562 + -0.3 m = 1.220655562 + -0.3 Combine like terms: 1.220655562 + -0.3 = 0.920655562 m = 0.920655562 Simplifying m = 0.920655562Subproblem 2
m + 0.3 = -1.220655562 Simplifying m + 0.3 = -1.220655562 Reorder the terms: 0.3 + m = -1.220655562 Solving 0.3 + m = -1.220655562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + m = -1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + m = -1.220655562 + -0.3 m = -1.220655562 + -0.3 Combine like terms: -1.220655562 + -0.3 = -1.520655562 m = -1.520655562 Simplifying m = -1.520655562Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.920655562, -1.520655562}
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