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Simplifying m(m + 3) = 234 Reorder the terms: m(3 + m) = 234 (3 * m + m * m) = 234 (3m + m2) = 234 Solving 3m + m2 = 234 Solving for variable 'm'. Reorder the terms: -234 + 3m + m2 = 234 + -234 Combine like terms: 234 + -234 = 0 -234 + 3m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '234' to each side of the equation. -234 + 3m + 234 + m2 = 0 + 234 Reorder the terms: -234 + 234 + 3m + m2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + 3m + m2 = 0 + 234 3m + m2 = 0 + 234 Combine like terms: 0 + 234 = 234 3m + m2 = 234 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 = 234 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 234 + 2.25 Combine like terms: 234 + 2.25 = 236.25 2.25 + 3m + m2 = 236.25 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (m + 1.5) equal to 15.370426149 and -15.370426149.Subproblem 1
m + 1.5 = 15.370426149 Simplifying m + 1.5 = 15.370426149 Reorder the terms: 1.5 + m = 15.370426149 Solving 1.5 + m = 15.370426149 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 = 15.370426149 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 15.370426149 + -1.5 m = 15.370426149 + -1.5 Combine like terms: 15.370426149 + -1.5 = 13.870426149 m = 13.870426149 Simplifying m = 13.870426149Subproblem 2
m + 1.5 = -15.370426149 Simplifying m + 1.5 = -15.370426149 Reorder the terms: 1.5 + m = -15.370426149 Solving 1.5 + m = -15.370426149 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 = -15.370426149 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -15.370426149 + -1.5 m = -15.370426149 + -1.5 Combine like terms: -15.370426149 + -1.5 = -16.870426149 m = -16.870426149 Simplifying m = -16.870426149Solution
The solution to the problem is based on the solutions from the subproblems. m = {13.870426149, -16.870426149}
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