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Simplifying m2 + -8m + -10 = 0 Reorder the terms: -10 + -8m + m2 = 0 Solving -10 + -8m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -8m + 10 + m2 = 0 + 10 Reorder the terms: -10 + 10 + -8m + m2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8m + m2 = 0 + 10 -8m + m2 = 0 + 10 Combine like terms: 0 + 10 = 10 -8m + m2 = 10 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 = 10 + 16 Reorder the terms: 16 + -8m + m2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + -8m + m2 = 26 Factor a perfect square on the left side: (m + -4)(m + -4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (m + -4) equal to 5.099019514 and -5.099019514.Subproblem 1
m + -4 = 5.099019514 Simplifying m + -4 = 5.099019514 Reorder the terms: -4 + m = 5.099019514 Solving -4 + m = 5.099019514 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 = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + m = 5.099019514 + 4 m = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 m = 9.099019514 Simplifying m = 9.099019514Subproblem 2
m + -4 = -5.099019514 Simplifying m + -4 = -5.099019514 Reorder the terms: -4 + m = -5.099019514 Solving -4 + m = -5.099019514 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 = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + m = -5.099019514 + 4 m = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 m = -1.099019514 Simplifying m = -1.099019514Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.099019514, -1.099019514}
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