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Simplifying m2 + -10m + 2 = 0 Reorder the terms: 2 + -10m + m2 = 0 Solving 2 + -10m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -10m + -2 + m2 = 0 + -2 Reorder the terms: 2 + -2 + -10m + m2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -10m + m2 = 0 + -2 -10m + m2 = 0 + -2 Combine like terms: 0 + -2 = -2 -10m + m2 = -2 The m term is -10m. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10m + 25 + m2 = -2 + 25 Reorder the terms: 25 + -10m + m2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + -10m + m2 = 23 Factor a perfect square on the left side: (m + -5)(m + -5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (m + -5) equal to 4.795831523 and -4.795831523.Subproblem 1
m + -5 = 4.795831523 Simplifying m + -5 = 4.795831523 Reorder the terms: -5 + m = 4.795831523 Solving -5 + m = 4.795831523 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + m = 4.795831523 + 5 m = 4.795831523 + 5 Combine like terms: 4.795831523 + 5 = 9.795831523 m = 9.795831523 Simplifying m = 9.795831523Subproblem 2
m + -5 = -4.795831523 Simplifying m + -5 = -4.795831523 Reorder the terms: -5 + m = -4.795831523 Solving -5 + m = -4.795831523 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + m = -4.795831523 + 5 m = -4.795831523 + 5 Combine like terms: -4.795831523 + 5 = 0.204168477 m = 0.204168477 Simplifying m = 0.204168477Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.795831523, 0.204168477}
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