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Simplifying m(m + -3) = 56 Reorder the terms: m(-3 + m) = 56 (-3 * m + m * m) = 56 (-3m + m2) = 56 Solving -3m + m2 = 56 Solving for variable 'm'. Reorder the terms: -56 + -3m + m2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -3m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -3m + 56 + m2 = 0 + 56 Reorder the terms: -56 + 56 + -3m + m2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -3m + m2 = 0 + 56 -3m + m2 = 0 + 56 Combine like terms: 0 + 56 = 56 -3m + m2 = 56 The m term is -3m. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3m + 2.25 + m2 = 56 + 2.25 Reorder the terms: 2.25 + -3m + m2 = 56 + 2.25 Combine like terms: 56 + 2.25 = 58.25 2.25 + -3m + m2 = 58.25 Factor a perfect square on the left side: (m + -1.5)(m + -1.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (m + -1.5) equal to 7.632168761 and -7.632168761.Subproblem 1
m + -1.5 = 7.632168761 Simplifying m + -1.5 = 7.632168761 Reorder the terms: -1.5 + m = 7.632168761 Solving -1.5 + m = 7.632168761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = 7.632168761 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = 7.632168761 + 1.5 m = 7.632168761 + 1.5 Combine like terms: 7.632168761 + 1.5 = 9.132168761 m = 9.132168761 Simplifying m = 9.132168761Subproblem 2
m + -1.5 = -7.632168761 Simplifying m + -1.5 = -7.632168761 Reorder the terms: -1.5 + m = -7.632168761 Solving -1.5 + m = -7.632168761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = -7.632168761 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = -7.632168761 + 1.5 m = -7.632168761 + 1.5 Combine like terms: -7.632168761 + 1.5 = -6.132168761 m = -6.132168761 Simplifying m = -6.132168761Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.132168761, -6.132168761}
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