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Simplifying m2 + -8m = 14 Reorder the terms: -8m + m2 = 14 Solving -8m + m2 = 14 Solving for variable 'm'. Reorder the terms: -14 + -8m + m2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -8m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + -8m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -8m + m2 = 0 + 14 -8m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 -8m + m2 = 14 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = 14 + 16 Reorder the terms: 16 + -8m + m2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + -8m + m2 = 30 Factor a perfect square on the left side: (m + -4)(m + -4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (m + -4) equal to 5.477225575 and -5.477225575.Subproblem 1
m + -4 = 5.477225575 Simplifying m + -4 = 5.477225575 Reorder the terms: -4 + m = 5.477225575 Solving -4 + m = 5.477225575 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 5.477225575 + 4 Combine like terms: -4 + 4 = 0 0 + m = 5.477225575 + 4 m = 5.477225575 + 4 Combine like terms: 5.477225575 + 4 = 9.477225575 m = 9.477225575 Simplifying m = 9.477225575Subproblem 2
m + -4 = -5.477225575 Simplifying m + -4 = -5.477225575 Reorder the terms: -4 + m = -5.477225575 Solving -4 + m = -5.477225575 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -5.477225575 + 4 Combine like terms: -4 + 4 = 0 0 + m = -5.477225575 + 4 m = -5.477225575 + 4 Combine like terms: -5.477225575 + 4 = -1.477225575 m = -1.477225575 Simplifying m = -1.477225575Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.477225575, -1.477225575}
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