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Simplifying m2 + -2m + -21 = 0 Reorder the terms: -21 + -2m + m2 = 0 Solving -21 + -2m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -2m + 21 + m2 = 0 + 21 Reorder the terms: -21 + 21 + -2m + m2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2m + m2 = 0 + 21 -2m + m2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2m + m2 = 21 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 = 21 + 1 Reorder the terms: 1 + -2m + m2 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + -2m + m2 = 22 Factor a perfect square on the left side: (m + -1)(m + -1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (m + -1) equal to 4.69041576 and -4.69041576.Subproblem 1
m + -1 = 4.69041576 Simplifying m + -1 = 4.69041576 Reorder the terms: -1 + m = 4.69041576 Solving -1 + m = 4.69041576 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 = 4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + m = 4.69041576 + 1 m = 4.69041576 + 1 Combine like terms: 4.69041576 + 1 = 5.69041576 m = 5.69041576 Simplifying m = 5.69041576Subproblem 2
m + -1 = -4.69041576 Simplifying m + -1 = -4.69041576 Reorder the terms: -1 + m = -4.69041576 Solving -1 + m = -4.69041576 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 = -4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + m = -4.69041576 + 1 m = -4.69041576 + 1 Combine like terms: -4.69041576 + 1 = -3.69041576 m = -3.69041576 Simplifying m = -3.69041576Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.69041576, -3.69041576}
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