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Simplifying -4m2 + 32m + -27 = 0 Reorder the terms: -27 + 32m + -4m2 = 0 Solving -27 + 32m + -4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 6.75 + -8m + m2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -8m + -6.75 + m2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -8m + m2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -8m + m2 = 0 + -6.75 -8m + m2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -8m + m2 = -6.75 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = -6.75 + 16 Reorder the terms: 16 + -8m + m2 = -6.75 + 16 Combine like terms: -6.75 + 16 = 9.25 16 + -8m + m2 = 9.25 Factor a perfect square on the left side: (m + -4)(m + -4) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (m + -4) equal to 3.041381265 and -3.041381265.Subproblem 1
m + -4 = 3.041381265 Simplifying m + -4 = 3.041381265 Reorder the terms: -4 + m = 3.041381265 Solving -4 + m = 3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 3.041381265 + 4 Combine like terms: -4 + 4 = 0 0 + m = 3.041381265 + 4 m = 3.041381265 + 4 Combine like terms: 3.041381265 + 4 = 7.041381265 m = 7.041381265 Simplifying m = 7.041381265Subproblem 2
m + -4 = -3.041381265 Simplifying m + -4 = -3.041381265 Reorder the terms: -4 + m = -3.041381265 Solving -4 + m = -3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -3.041381265 + 4 Combine like terms: -4 + 4 = 0 0 + m = -3.041381265 + 4 m = -3.041381265 + 4 Combine like terms: -3.041381265 + 4 = 0.958618735 m = 0.958618735 Simplifying m = 0.958618735Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.041381265, 0.958618735}
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