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Simplifying 8m2 + -3m + -18 = 0 Reorder the terms: -18 + -3m + 8m2 = 0 Solving -18 + -3m + 8m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + -0.375m + m2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.375m + 2.25 + m2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.375m + m2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.375m + m2 = 0 + 2.25 -0.375m + m2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.375m + m2 = 2.25 The m term is -0.375m. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375m + 0.03515625 + m2 = 2.25 + 0.03515625 Reorder the terms: 0.03515625 + -0.375m + m2 = 2.25 + 0.03515625 Combine like terms: 2.25 + 0.03515625 = 2.28515625 0.03515625 + -0.375m + m2 = 2.28515625 Factor a perfect square on the left side: (m + -0.1875)(m + -0.1875) = 2.28515625 Calculate the square root of the right side: 1.511673328 Break this problem into two subproblems by setting (m + -0.1875) equal to 1.511673328 and -1.511673328.Subproblem 1
m + -0.1875 = 1.511673328 Simplifying m + -0.1875 = 1.511673328 Reorder the terms: -0.1875 + m = 1.511673328 Solving -0.1875 + m = 1.511673328 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + m = 1.511673328 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + m = 1.511673328 + 0.1875 m = 1.511673328 + 0.1875 Combine like terms: 1.511673328 + 0.1875 = 1.699173328 m = 1.699173328 Simplifying m = 1.699173328Subproblem 2
m + -0.1875 = -1.511673328 Simplifying m + -0.1875 = -1.511673328 Reorder the terms: -0.1875 + m = -1.511673328 Solving -0.1875 + m = -1.511673328 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + m = -1.511673328 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + m = -1.511673328 + 0.1875 m = -1.511673328 + 0.1875 Combine like terms: -1.511673328 + 0.1875 = -1.324173328 m = -1.324173328 Simplifying m = -1.324173328Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.699173328, -1.324173328}
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