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Simplifying 8m2 + 2m = 9 Reorder the terms: 2m + 8m2 = 9 Solving 2m + 8m2 = 9 Solving for variable 'm'. Reorder the terms: -9 + 2m + 8m2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 2m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 0.25m + m2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.25m + 1.125 + m2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.25m + m2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.25m + m2 = 0 + 1.125 0.25m + m2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.25m + m2 = 1.125 The m term is 0.25m. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25m + 0.015625 + m2 = 1.125 + 0.015625 Reorder the terms: 0.015625 + 0.25m + m2 = 1.125 + 0.015625 Combine like terms: 1.125 + 0.015625 = 1.140625 0.015625 + 0.25m + m2 = 1.140625 Factor a perfect square on the left side: (m + 0.125)(m + 0.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (m + 0.125) equal to 1.068000468 and -1.068000468.Subproblem 1
m + 0.125 = 1.068000468 Simplifying m + 0.125 = 1.068000468 Reorder the terms: 0.125 + m = 1.068000468 Solving 0.125 + m = 1.068000468 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = 1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = 1.068000468 + -0.125 m = 1.068000468 + -0.125 Combine like terms: 1.068000468 + -0.125 = 0.943000468 m = 0.943000468 Simplifying m = 0.943000468Subproblem 2
m + 0.125 = -1.068000468 Simplifying m + 0.125 = -1.068000468 Reorder the terms: 0.125 + m = -1.068000468 Solving 0.125 + m = -1.068000468 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = -1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = -1.068000468 + -0.125 m = -1.068000468 + -0.125 Combine like terms: -1.068000468 + -0.125 = -1.193000468 m = -1.193000468 Simplifying m = -1.193000468Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.943000468, -1.193000468}
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