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Simplifying m2 + -70 = 14m Reorder the terms: -70 + m2 = 14m Solving -70 + m2 = 14m Solving for variable 'm'. Reorder the terms: -70 + -14m + m2 = 14m + -14m Combine like terms: 14m + -14m = 0 -70 + -14m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -14m + 70 + m2 = 0 + 70 Reorder the terms: -70 + 70 + -14m + m2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -14m + m2 = 0 + 70 -14m + m2 = 0 + 70 Combine like terms: 0 + 70 = 70 -14m + m2 = 70 The m term is -14m. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14m + 49 + m2 = 70 + 49 Reorder the terms: 49 + -14m + m2 = 70 + 49 Combine like terms: 70 + 49 = 119 49 + -14m + m2 = 119 Factor a perfect square on the left side: (m + -7)(m + -7) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (m + -7) equal to 10.908712115 and -10.908712115.Subproblem 1
m + -7 = 10.908712115 Simplifying m + -7 = 10.908712115 Reorder the terms: -7 + m = 10.908712115 Solving -7 + m = 10.908712115 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = 10.908712115 + 7 Combine like terms: -7 + 7 = 0 0 + m = 10.908712115 + 7 m = 10.908712115 + 7 Combine like terms: 10.908712115 + 7 = 17.908712115 m = 17.908712115 Simplifying m = 17.908712115Subproblem 2
m + -7 = -10.908712115 Simplifying m + -7 = -10.908712115 Reorder the terms: -7 + m = -10.908712115 Solving -7 + m = -10.908712115 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = -10.908712115 + 7 Combine like terms: -7 + 7 = 0 0 + m = -10.908712115 + 7 m = -10.908712115 + 7 Combine like terms: -10.908712115 + 7 = -3.908712115 m = -3.908712115 Simplifying m = -3.908712115Solution
The solution to the problem is based on the solutions from the subproblems. m = {17.908712115, -3.908712115}
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