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Simplifying m2 + 26m + 45 = 0 Reorder the terms: 45 + 26m + m2 = 0 Solving 45 + 26m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 26m + -45 + m2 = 0 + -45 Reorder the terms: 45 + -45 + 26m + m2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 26m + m2 = 0 + -45 26m + m2 = 0 + -45 Combine like terms: 0 + -45 = -45 26m + m2 = -45 The m term is 26m. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26m + 169 + m2 = -45 + 169 Reorder the terms: 169 + 26m + m2 = -45 + 169 Combine like terms: -45 + 169 = 124 169 + 26m + m2 = 124 Factor a perfect square on the left side: (m + 13)(m + 13) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (m + 13) equal to 11.135528726 and -11.135528726.Subproblem 1
m + 13 = 11.135528726 Simplifying m + 13 = 11.135528726 Reorder the terms: 13 + m = 11.135528726 Solving 13 + m = 11.135528726 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + m = 11.135528726 + -13 Combine like terms: 13 + -13 = 0 0 + m = 11.135528726 + -13 m = 11.135528726 + -13 Combine like terms: 11.135528726 + -13 = -1.864471274 m = -1.864471274 Simplifying m = -1.864471274Subproblem 2
m + 13 = -11.135528726 Simplifying m + 13 = -11.135528726 Reorder the terms: 13 + m = -11.135528726 Solving 13 + m = -11.135528726 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + m = -11.135528726 + -13 Combine like terms: 13 + -13 = 0 0 + m = -11.135528726 + -13 m = -11.135528726 + -13 Combine like terms: -11.135528726 + -13 = -24.135528726 m = -24.135528726 Simplifying m = -24.135528726Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.864471274, -24.135528726}
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