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Simplifying 5m + -2m(m + -5) = 19 Reorder the terms: 5m + -2m(-5 + m) = 19 5m + (-5 * -2m + m * -2m) = 19 5m + (10m + -2m2) = 19 Combine like terms: 5m + 10m = 15m 15m + -2m2 = 19 Solving 15m + -2m2 = 19 Solving for variable 'm'. Reorder the terms: -19 + 15m + -2m2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 15m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 9.5 + -7.5m + m2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + -7.5m + -9.5 + m2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + -7.5m + m2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -7.5m + m2 = 0 + -9.5 -7.5m + m2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 -7.5m + m2 = -9.5 The m term is -7.5m. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5m + 14.0625 + m2 = -9.5 + 14.0625 Reorder the terms: 14.0625 + -7.5m + m2 = -9.5 + 14.0625 Combine like terms: -9.5 + 14.0625 = 4.5625 14.0625 + -7.5m + m2 = 4.5625 Factor a perfect square on the left side: (m + -3.75)(m + -3.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (m + -3.75) equal to 2.136000936 and -2.136000936.Subproblem 1
m + -3.75 = 2.136000936 Simplifying m + -3.75 = 2.136000936 Reorder the terms: -3.75 + m = 2.136000936 Solving -3.75 + m = 2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + m = 2.136000936 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + m = 2.136000936 + 3.75 m = 2.136000936 + 3.75 Combine like terms: 2.136000936 + 3.75 = 5.886000936 m = 5.886000936 Simplifying m = 5.886000936Subproblem 2
m + -3.75 = -2.136000936 Simplifying m + -3.75 = -2.136000936 Reorder the terms: -3.75 + m = -2.136000936 Solving -3.75 + m = -2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + m = -2.136000936 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + m = -2.136000936 + 3.75 m = -2.136000936 + 3.75 Combine like terms: -2.136000936 + 3.75 = 1.613999064 m = 1.613999064 Simplifying m = 1.613999064Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.886000936, 1.613999064}
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