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Simplifying -4m(m + -9) = 3m + -6 Reorder the terms: -4m(-9 + m) = 3m + -6 (-9 * -4m + m * -4m) = 3m + -6 (36m + -4m2) = 3m + -6 Reorder the terms: 36m + -4m2 = -6 + 3m Solving 36m + -4m2 = -6 + 3m Solving for variable 'm'. Reorder the terms: 6 + 36m + -3m + -4m2 = -6 + 3m + 6 + -3m Combine like terms: 36m + -3m = 33m 6 + 33m + -4m2 = -6 + 3m + 6 + -3m Reorder the terms: 6 + 33m + -4m2 = -6 + 6 + 3m + -3m Combine like terms: -6 + 6 = 0 6 + 33m + -4m2 = 0 + 3m + -3m 6 + 33m + -4m2 = 3m + -3m Combine like terms: 3m + -3m = 0 6 + 33m + -4m2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.5 + -8.25m + m2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -8.25m + 1.5 + m2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -8.25m + m2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -8.25m + m2 = 0 + 1.5 -8.25m + m2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -8.25m + m2 = 1.5 The m term is -8.25m. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25m + 17.015625 + m2 = 1.5 + 17.015625 Reorder the terms: 17.015625 + -8.25m + m2 = 1.5 + 17.015625 Combine like terms: 1.5 + 17.015625 = 18.515625 17.015625 + -8.25m + m2 = 18.515625 Factor a perfect square on the left side: (m + -4.125)(m + -4.125) = 18.515625 Calculate the square root of the right side: 4.30297862 Break this problem into two subproblems by setting (m + -4.125) equal to 4.30297862 and -4.30297862.Subproblem 1
m + -4.125 = 4.30297862 Simplifying m + -4.125 = 4.30297862 Reorder the terms: -4.125 + m = 4.30297862 Solving -4.125 + m = 4.30297862 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + m = 4.30297862 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + m = 4.30297862 + 4.125 m = 4.30297862 + 4.125 Combine like terms: 4.30297862 + 4.125 = 8.42797862 m = 8.42797862 Simplifying m = 8.42797862Subproblem 2
m + -4.125 = -4.30297862 Simplifying m + -4.125 = -4.30297862 Reorder the terms: -4.125 + m = -4.30297862 Solving -4.125 + m = -4.30297862 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + m = -4.30297862 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + m = -4.30297862 + 4.125 m = -4.30297862 + 4.125 Combine like terms: -4.30297862 + 4.125 = -0.17797862 m = -0.17797862 Simplifying m = -0.17797862Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.42797862, -0.17797862}
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