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Simplifying 8m2 + 11m = 15 Reorder the terms: 11m + 8m2 = 15 Solving 11m + 8m2 = 15 Solving for variable 'm'. Reorder the terms: -15 + 11m + 8m2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 11m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + 1.375m + m2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 1.375m + 1.875 + m2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 1.375m + m2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 1.375m + m2 = 0 + 1.875 1.375m + m2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 1.375m + m2 = 1.875 The m term is 1.375m. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375m + 0.47265625 + m2 = 1.875 + 0.47265625 Reorder the terms: 0.47265625 + 1.375m + m2 = 1.875 + 0.47265625 Combine like terms: 1.875 + 0.47265625 = 2.34765625 0.47265625 + 1.375m + m2 = 2.34765625 Factor a perfect square on the left side: (m + 0.6875)(m + 0.6875) = 2.34765625 Calculate the square root of the right side: 1.532206334 Break this problem into two subproblems by setting (m + 0.6875) equal to 1.532206334 and -1.532206334.Subproblem 1
m + 0.6875 = 1.532206334 Simplifying m + 0.6875 = 1.532206334 Reorder the terms: 0.6875 + m = 1.532206334 Solving 0.6875 + m = 1.532206334 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + m = 1.532206334 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + m = 1.532206334 + -0.6875 m = 1.532206334 + -0.6875 Combine like terms: 1.532206334 + -0.6875 = 0.844706334 m = 0.844706334 Simplifying m = 0.844706334Subproblem 2
m + 0.6875 = -1.532206334 Simplifying m + 0.6875 = -1.532206334 Reorder the terms: 0.6875 + m = -1.532206334 Solving 0.6875 + m = -1.532206334 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + m = -1.532206334 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + m = -1.532206334 + -0.6875 m = -1.532206334 + -0.6875 Combine like terms: -1.532206334 + -0.6875 = -2.219706334 m = -2.219706334 Simplifying m = -2.219706334Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.844706334, -2.219706334}
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