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Simplifying m2 + -12m + -89 = 0 Reorder the terms: -89 + -12m + m2 = 0 Solving -89 + -12m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + -12m + 89 + m2 = 0 + 89 Reorder the terms: -89 + 89 + -12m + m2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + -12m + m2 = 0 + 89 -12m + m2 = 0 + 89 Combine like terms: 0 + 89 = 89 -12m + m2 = 89 The m term is -12m. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12m + 36 + m2 = 89 + 36 Reorder the terms: 36 + -12m + m2 = 89 + 36 Combine like terms: 89 + 36 = 125 36 + -12m + m2 = 125 Factor a perfect square on the left side: (m + -6)(m + -6) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (m + -6) equal to 11.180339887 and -11.180339887.Subproblem 1
m + -6 = 11.180339887 Simplifying m + -6 = 11.180339887 Reorder the terms: -6 + m = 11.180339887 Solving -6 + m = 11.180339887 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = 11.180339887 + 6 Combine like terms: -6 + 6 = 0 0 + m = 11.180339887 + 6 m = 11.180339887 + 6 Combine like terms: 11.180339887 + 6 = 17.180339887 m = 17.180339887 Simplifying m = 17.180339887Subproblem 2
m + -6 = -11.180339887 Simplifying m + -6 = -11.180339887 Reorder the terms: -6 + m = -11.180339887 Solving -6 + m = -11.180339887 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = -11.180339887 + 6 Combine like terms: -6 + 6 = 0 0 + m = -11.180339887 + 6 m = -11.180339887 + 6 Combine like terms: -11.180339887 + 6 = -5.180339887 m = -5.180339887 Simplifying m = -5.180339887Solution
The solution to the problem is based on the solutions from the subproblems. m = {17.180339887, -5.180339887}
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