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Simplifying m2 + -4m + -66 = 0 Reorder the terms: -66 + -4m + m2 = 0 Solving -66 + -4m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + -4m + 66 + m2 = 0 + 66 Reorder the terms: -66 + 66 + -4m + m2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + -4m + m2 = 0 + 66 -4m + m2 = 0 + 66 Combine like terms: 0 + 66 = 66 -4m + m2 = 66 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 66 + 4 Reorder the terms: 4 + -4m + m2 = 66 + 4 Combine like terms: 66 + 4 = 70 4 + -4m + m2 = 70 Factor a perfect square on the left side: (m + -2)(m + -2) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (m + -2) equal to 8.366600265 and -8.366600265.Subproblem 1
m + -2 = 8.366600265 Simplifying m + -2 = 8.366600265 Reorder the terms: -2 + m = 8.366600265 Solving -2 + m = 8.366600265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 8.366600265 + 2 Combine like terms: -2 + 2 = 0 0 + m = 8.366600265 + 2 m = 8.366600265 + 2 Combine like terms: 8.366600265 + 2 = 10.366600265 m = 10.366600265 Simplifying m = 10.366600265Subproblem 2
m + -2 = -8.366600265 Simplifying m + -2 = -8.366600265 Reorder the terms: -2 + m = -8.366600265 Solving -2 + m = -8.366600265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -8.366600265 + 2 Combine like terms: -2 + 2 = 0 0 + m = -8.366600265 + 2 m = -8.366600265 + 2 Combine like terms: -8.366600265 + 2 = -6.366600265 m = -6.366600265 Simplifying m = -6.366600265Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.366600265, -6.366600265}
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