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Simplifying m2 + -20m + -14 = 0 Reorder the terms: -14 + -20m + m2 = 0 Solving -14 + -20m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -20m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + -20m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -20m + m2 = 0 + 14 -20m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 -20m + m2 = 14 The m term is -20m. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20m + 100 + m2 = 14 + 100 Reorder the terms: 100 + -20m + m2 = 14 + 100 Combine like terms: 14 + 100 = 114 100 + -20m + m2 = 114 Factor a perfect square on the left side: (m + -10)(m + -10) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (m + -10) equal to 10.677078252 and -10.677078252.Subproblem 1
m + -10 = 10.677078252 Simplifying m + -10 = 10.677078252 Reorder the terms: -10 + m = 10.677078252 Solving -10 + m = 10.677078252 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = 10.677078252 + 10 Combine like terms: -10 + 10 = 0 0 + m = 10.677078252 + 10 m = 10.677078252 + 10 Combine like terms: 10.677078252 + 10 = 20.677078252 m = 20.677078252 Simplifying m = 20.677078252Subproblem 2
m + -10 = -10.677078252 Simplifying m + -10 = -10.677078252 Reorder the terms: -10 + m = -10.677078252 Solving -10 + m = -10.677078252 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = -10.677078252 + 10 Combine like terms: -10 + 10 = 0 0 + m = -10.677078252 + 10 m = -10.677078252 + 10 Combine like terms: -10.677078252 + 10 = -0.677078252 m = -0.677078252 Simplifying m = -0.677078252Solution
The solution to the problem is based on the solutions from the subproblems. m = {20.677078252, -0.677078252}
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