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Simplifying m2 + -12 + 12m + 26 = 0 Reorder the terms: -12 + 26 + 12m + m2 = 0 Combine like terms: -12 + 26 = 14 14 + 12m + m2 = 0 Solving 14 + 12m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 12m + -14 + m2 = 0 + -14 Reorder the terms: 14 + -14 + 12m + m2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 12m + m2 = 0 + -14 12m + m2 = 0 + -14 Combine like terms: 0 + -14 = -14 12m + m2 = -14 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 = -14 + 36 Reorder the terms: 36 + 12m + m2 = -14 + 36 Combine like terms: -14 + 36 = 22 36 + 12m + m2 = 22 Factor a perfect square on the left side: (m + 6)(m + 6) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (m + 6) equal to 4.69041576 and -4.69041576.Subproblem 1
m + 6 = 4.69041576 Simplifying m + 6 = 4.69041576 Reorder the terms: 6 + m = 4.69041576 Solving 6 + m = 4.69041576 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 = 4.69041576 + -6 Combine like terms: 6 + -6 = 0 0 + m = 4.69041576 + -6 m = 4.69041576 + -6 Combine like terms: 4.69041576 + -6 = -1.30958424 m = -1.30958424 Simplifying m = -1.30958424Subproblem 2
m + 6 = -4.69041576 Simplifying m + 6 = -4.69041576 Reorder the terms: 6 + m = -4.69041576 Solving 6 + m = -4.69041576 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 = -4.69041576 + -6 Combine like terms: 6 + -6 = 0 0 + m = -4.69041576 + -6 m = -4.69041576 + -6 Combine like terms: -4.69041576 + -6 = -10.69041576 m = -10.69041576 Simplifying m = -10.69041576Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.30958424, -10.69041576}
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