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Simplifying 8m2 + -3m + -6 = 0 Reorder the terms: -6 + -3m + 8m2 = 0 Solving -6 + -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'. -0.75 + -0.375m + m2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.375m + 0.75 + m2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.375m + m2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.375m + m2 = 0 + 0.75 -0.375m + m2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.375m + m2 = 0.75 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 = 0.75 + 0.03515625 Reorder the terms: 0.03515625 + -0.375m + m2 = 0.75 + 0.03515625 Combine like terms: 0.75 + 0.03515625 = 0.78515625 0.03515625 + -0.375m + m2 = 0.78515625 Factor a perfect square on the left side: (m + -0.1875)(m + -0.1875) = 0.78515625 Calculate the square root of the right side: 0.88609043 Break this problem into two subproblems by setting (m + -0.1875) equal to 0.88609043 and -0.88609043.Subproblem 1
m + -0.1875 = 0.88609043 Simplifying m + -0.1875 = 0.88609043 Reorder the terms: -0.1875 + m = 0.88609043 Solving -0.1875 + m = 0.88609043 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 = 0.88609043 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + m = 0.88609043 + 0.1875 m = 0.88609043 + 0.1875 Combine like terms: 0.88609043 + 0.1875 = 1.07359043 m = 1.07359043 Simplifying m = 1.07359043Subproblem 2
m + -0.1875 = -0.88609043 Simplifying m + -0.1875 = -0.88609043 Reorder the terms: -0.1875 + m = -0.88609043 Solving -0.1875 + m = -0.88609043 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 = -0.88609043 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + m = -0.88609043 + 0.1875 m = -0.88609043 + 0.1875 Combine like terms: -0.88609043 + 0.1875 = -0.69859043 m = -0.69859043 Simplifying m = -0.69859043Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.07359043, -0.69859043}
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