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Simplifying -4m2 + -23m + 36 = 0 Reorder the terms: 36 + -23m + -4m2 = 0 Solving 36 + -23m + -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'. -9 + 5.75m + m2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 5.75m + 9 + m2 = 0 + 9 Reorder the terms: -9 + 9 + 5.75m + m2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5.75m + m2 = 0 + 9 5.75m + m2 = 0 + 9 Combine like terms: 0 + 9 = 9 5.75m + m2 = 9 The m term is 5.75m. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75m + 8.265625 + m2 = 9 + 8.265625 Reorder the terms: 8.265625 + 5.75m + m2 = 9 + 8.265625 Combine like terms: 9 + 8.265625 = 17.265625 8.265625 + 5.75m + m2 = 17.265625 Factor a perfect square on the left side: (m + 2.875)(m + 2.875) = 17.265625 Calculate the square root of the right side: 4.155192535 Break this problem into two subproblems by setting (m + 2.875) equal to 4.155192535 and -4.155192535.Subproblem 1
m + 2.875 = 4.155192535 Simplifying m + 2.875 = 4.155192535 Reorder the terms: 2.875 + m = 4.155192535 Solving 2.875 + m = 4.155192535 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + m = 4.155192535 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + m = 4.155192535 + -2.875 m = 4.155192535 + -2.875 Combine like terms: 4.155192535 + -2.875 = 1.280192535 m = 1.280192535 Simplifying m = 1.280192535Subproblem 2
m + 2.875 = -4.155192535 Simplifying m + 2.875 = -4.155192535 Reorder the terms: 2.875 + m = -4.155192535 Solving 2.875 + m = -4.155192535 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + m = -4.155192535 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + m = -4.155192535 + -2.875 m = -4.155192535 + -2.875 Combine like terms: -4.155192535 + -2.875 = -7.030192535 m = -7.030192535 Simplifying m = -7.030192535Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.280192535, -7.030192535}
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