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Simplifying m2 + -8m + -80 = 0 Reorder the terms: -80 + -8m + m2 = 0 Solving -80 + -8m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -8m + 80 + m2 = 0 + 80 Reorder the terms: -80 + 80 + -8m + m2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -8m + m2 = 0 + 80 -8m + m2 = 0 + 80 Combine like terms: 0 + 80 = 80 -8m + m2 = 80 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = 80 + 16 Reorder the terms: 16 + -8m + m2 = 80 + 16 Combine like terms: 80 + 16 = 96 16 + -8m + m2 = 96 Factor a perfect square on the left side: (m + -4)(m + -4) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (m + -4) equal to 9.797958971 and -9.797958971.Subproblem 1
m + -4 = 9.797958971 Simplifying m + -4 = 9.797958971 Reorder the terms: -4 + m = 9.797958971 Solving -4 + m = 9.797958971 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + m = 9.797958971 + 4 m = 9.797958971 + 4 Combine like terms: 9.797958971 + 4 = 13.797958971 m = 13.797958971 Simplifying m = 13.797958971Subproblem 2
m + -4 = -9.797958971 Simplifying m + -4 = -9.797958971 Reorder the terms: -4 + m = -9.797958971 Solving -4 + m = -9.797958971 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + m = -9.797958971 + 4 m = -9.797958971 + 4 Combine like terms: -9.797958971 + 4 = -5.797958971 m = -5.797958971 Simplifying m = -5.797958971Solution
The solution to the problem is based on the solutions from the subproblems. m = {13.797958971, -5.797958971}
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