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Simplifying m2 + -18m = 35 Reorder the terms: -18m + m2 = 35 Solving -18m + m2 = 35 Solving for variable 'm'. Reorder the terms: -35 + -18m + m2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -18m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -18m + 35 + m2 = 0 + 35 Reorder the terms: -35 + 35 + -18m + m2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -18m + m2 = 0 + 35 -18m + m2 = 0 + 35 Combine like terms: 0 + 35 = 35 -18m + m2 = 35 The m term is -18m. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18m + 81 + m2 = 35 + 81 Reorder the terms: 81 + -18m + m2 = 35 + 81 Combine like terms: 35 + 81 = 116 81 + -18m + m2 = 116 Factor a perfect square on the left side: (m + -9)(m + -9) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (m + -9) equal to 10.770329614 and -10.770329614.Subproblem 1
m + -9 = 10.770329614 Simplifying m + -9 = 10.770329614 Reorder the terms: -9 + m = 10.770329614 Solving -9 + m = 10.770329614 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + m = 10.770329614 + 9 Combine like terms: -9 + 9 = 0 0 + m = 10.770329614 + 9 m = 10.770329614 + 9 Combine like terms: 10.770329614 + 9 = 19.770329614 m = 19.770329614 Simplifying m = 19.770329614Subproblem 2
m + -9 = -10.770329614 Simplifying m + -9 = -10.770329614 Reorder the terms: -9 + m = -10.770329614 Solving -9 + m = -10.770329614 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + m = -10.770329614 + 9 Combine like terms: -9 + 9 = 0 0 + m = -10.770329614 + 9 m = -10.770329614 + 9 Combine like terms: -10.770329614 + 9 = -1.770329614 m = -1.770329614 Simplifying m = -1.770329614Solution
The solution to the problem is based on the solutions from the subproblems. m = {19.770329614, -1.770329614}
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