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Simplifying m2 + -1m + -68 = 0 Reorder the terms: -68 + -1m + m2 = 0 Solving -68 + -1m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + -1m + 68 + m2 = 0 + 68 Reorder the terms: -68 + 68 + -1m + m2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + -1m + m2 = 0 + 68 -1m + m2 = 0 + 68 Combine like terms: 0 + 68 = 68 -1m + m2 = 68 The m term is -1m. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1m + 0.25 + m2 = 68 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 68 + 0.25 Combine like terms: 68 + 0.25 = 68.25 0.25 + -1m + m2 = 68.25 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (m + -0.5) equal to 8.261355821 and -8.261355821.Subproblem 1
m + -0.5 = 8.261355821 Simplifying m + -0.5 = 8.261355821 Reorder the terms: -0.5 + m = 8.261355821 Solving -0.5 + m = 8.261355821 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = 8.261355821 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 8.261355821 + 0.5 m = 8.261355821 + 0.5 Combine like terms: 8.261355821 + 0.5 = 8.761355821 m = 8.761355821 Simplifying m = 8.761355821Subproblem 2
m + -0.5 = -8.261355821 Simplifying m + -0.5 = -8.261355821 Reorder the terms: -0.5 + m = -8.261355821 Solving -0.5 + m = -8.261355821 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = -8.261355821 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -8.261355821 + 0.5 m = -8.261355821 + 0.5 Combine like terms: -8.261355821 + 0.5 = -7.761355821 m = -7.761355821 Simplifying m = -7.761355821Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.761355821, -7.761355821}
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