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Simplifying 8m2 + -2m = 7 Reorder the terms: -2m + 8m2 = 7 Solving -2m + 8m2 = 7 Solving for variable 'm'. Reorder the terms: -7 + -2m + 8m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -2m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.25m + m2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.25m + 0.875 + m2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.25m + m2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.25m + m2 = 0 + 0.875 -0.25m + m2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.25m + m2 = 0.875 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 = 0.875 + 0.015625 Reorder the terms: 0.015625 + -0.25m + m2 = 0.875 + 0.015625 Combine like terms: 0.875 + 0.015625 = 0.890625 0.015625 + -0.25m + m2 = 0.890625 Factor a perfect square on the left side: (m + -0.125)(m + -0.125) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (m + -0.125) equal to 0.943729304 and -0.943729304.Subproblem 1
m + -0.125 = 0.943729304 Simplifying m + -0.125 = 0.943729304 Reorder the terms: -0.125 + m = 0.943729304 Solving -0.125 + m = 0.943729304 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 = 0.943729304 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + m = 0.943729304 + 0.125 m = 0.943729304 + 0.125 Combine like terms: 0.943729304 + 0.125 = 1.068729304 m = 1.068729304 Simplifying m = 1.068729304Subproblem 2
m + -0.125 = -0.943729304 Simplifying m + -0.125 = -0.943729304 Reorder the terms: -0.125 + m = -0.943729304 Solving -0.125 + m = -0.943729304 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 = -0.943729304 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + m = -0.943729304 + 0.125 m = -0.943729304 + 0.125 Combine like terms: -0.943729304 + 0.125 = -0.818729304 m = -0.818729304 Simplifying m = -0.818729304Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.068729304, -0.818729304}
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