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Simplifying m2 + -2m + -10 = 0 Reorder the terms: -10 + -2m + m2 = 0 Solving -10 + -2m + 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 + -2m + 10 + m2 = 0 + 10 Reorder the terms: -10 + 10 + -2m + m2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2m + m2 = 0 + 10 -2m + m2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2m + m2 = 10 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 10 + 1 Reorder the terms: 1 + -2m + m2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2m + m2 = 11 Factor a perfect square on the left side: (m + -1)(m + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (m + -1) equal to 3.31662479 and -3.31662479.Subproblem 1
m + -1 = 3.31662479 Simplifying m + -1 = 3.31662479 Reorder the terms: -1 + m = 3.31662479 Solving -1 + m = 3.31662479 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + m = 3.31662479 + 1 m = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 m = 4.31662479 Simplifying m = 4.31662479Subproblem 2
m + -1 = -3.31662479 Simplifying m + -1 = -3.31662479 Reorder the terms: -1 + m = -3.31662479 Solving -1 + m = -3.31662479 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + m = -3.31662479 + 1 m = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 m = -2.31662479 Simplifying m = -2.31662479Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.31662479, -2.31662479}
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