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Simplifying 9(m + 8) = 8(m + 9) * m Reorder the terms: 9(8 + m) = 8(m + 9) * m (8 * 9 + m * 9) = 8(m + 9) * m (72 + 9m) = 8(m + 9) * m Reorder the terms: 72 + 9m = 8(9 + m) * m Reorder the terms for easier multiplication: 72 + 9m = 8m(9 + m) 72 + 9m = (9 * 8m + m * 8m) 72 + 9m = (72m + 8m2) Solving 72 + 9m = 72m + 8m2 Solving for variable 'm'. Combine like terms: 9m + -72m = -63m 72 + -63m + -8m2 = 72m + 8m2 + -72m + -8m2 Reorder the terms: 72 + -63m + -8m2 = 72m + -72m + 8m2 + -8m2 Combine like terms: 72m + -72m = 0 72 + -63m + -8m2 = 0 + 8m2 + -8m2 72 + -63m + -8m2 = 8m2 + -8m2 Combine like terms: 8m2 + -8m2 = 0 72 + -63m + -8m2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9 + 7.875m + m2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 7.875m + 9 + m2 = 0 + 9 Reorder the terms: -9 + 9 + 7.875m + m2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 7.875m + m2 = 0 + 9 7.875m + m2 = 0 + 9 Combine like terms: 0 + 9 = 9 7.875m + m2 = 9 The m term is 7.875m. Take half its coefficient (3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. 7.875m + 15.50390625 + m2 = 9 + 15.50390625 Reorder the terms: 15.50390625 + 7.875m + m2 = 9 + 15.50390625 Combine like terms: 9 + 15.50390625 = 24.50390625 15.50390625 + 7.875m + m2 = 24.50390625 Factor a perfect square on the left side: (m + 3.9375)(m + 3.9375) = 24.50390625 Calculate the square root of the right side: 4.950142043 Break this problem into two subproblems by setting (m + 3.9375) equal to 4.950142043 and -4.950142043.Subproblem 1
m + 3.9375 = 4.950142043 Simplifying m + 3.9375 = 4.950142043 Reorder the terms: 3.9375 + m = 4.950142043 Solving 3.9375 + m = 4.950142043 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + m = 4.950142043 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + m = 4.950142043 + -3.9375 m = 4.950142043 + -3.9375 Combine like terms: 4.950142043 + -3.9375 = 1.012642043 m = 1.012642043 Simplifying m = 1.012642043Subproblem 2
m + 3.9375 = -4.950142043 Simplifying m + 3.9375 = -4.950142043 Reorder the terms: 3.9375 + m = -4.950142043 Solving 3.9375 + m = -4.950142043 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + m = -4.950142043 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + m = -4.950142043 + -3.9375 m = -4.950142043 + -3.9375 Combine like terms: -4.950142043 + -3.9375 = -8.887642043 m = -8.887642043 Simplifying m = -8.887642043Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.012642043, -8.887642043}
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