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Simplifying m2 + -1m + -14 = 0 Reorder the terms: -14 + -1m + m2 = 0 Solving -14 + -1m + 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 + -1m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + -1m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1m + m2 = 0 + 14 -1m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 -1m + m2 = 14 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 = 14 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + -1m + m2 = 14.25 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (m + -0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
m + -0.5 = 3.774917218 Simplifying m + -0.5 = 3.774917218 Reorder the terms: -0.5 + m = 3.774917218 Solving -0.5 + m = 3.774917218 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 = 3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 3.774917218 + 0.5 m = 3.774917218 + 0.5 Combine like terms: 3.774917218 + 0.5 = 4.274917218 m = 4.274917218 Simplifying m = 4.274917218Subproblem 2
m + -0.5 = -3.774917218 Simplifying m + -0.5 = -3.774917218 Reorder the terms: -0.5 + m = -3.774917218 Solving -0.5 + m = -3.774917218 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 = -3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -3.774917218 + 0.5 m = -3.774917218 + 0.5 Combine like terms: -3.774917218 + 0.5 = -3.274917218 m = -3.274917218 Simplifying m = -3.274917218Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.274917218, -3.274917218}
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