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Simplifying m2 + 22 = -22m Reorder the terms: 22 + m2 = -22m Solving 22 + m2 = -22m Solving for variable 'm'. Reorder the terms: 22 + 22m + m2 = -22m + 22m Combine like terms: -22m + 22m = 0 22 + 22m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 22m + -22 + m2 = 0 + -22 Reorder the terms: 22 + -22 + 22m + m2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 22m + m2 = 0 + -22 22m + m2 = 0 + -22 Combine like terms: 0 + -22 = -22 22m + m2 = -22 The m term is 22m. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22m + 121 + m2 = -22 + 121 Reorder the terms: 121 + 22m + m2 = -22 + 121 Combine like terms: -22 + 121 = 99 121 + 22m + m2 = 99 Factor a perfect square on the left side: (m + 11)(m + 11) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (m + 11) equal to 9.949874371 and -9.949874371.Subproblem 1
m + 11 = 9.949874371 Simplifying m + 11 = 9.949874371 Reorder the terms: 11 + m = 9.949874371 Solving 11 + m = 9.949874371 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + m = 9.949874371 + -11 Combine like terms: 11 + -11 = 0 0 + m = 9.949874371 + -11 m = 9.949874371 + -11 Combine like terms: 9.949874371 + -11 = -1.050125629 m = -1.050125629 Simplifying m = -1.050125629Subproblem 2
m + 11 = -9.949874371 Simplifying m + 11 = -9.949874371 Reorder the terms: 11 + m = -9.949874371 Solving 11 + m = -9.949874371 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + m = -9.949874371 + -11 Combine like terms: 11 + -11 = 0 0 + m = -9.949874371 + -11 m = -9.949874371 + -11 Combine like terms: -9.949874371 + -11 = -20.949874371 m = -20.949874371 Simplifying m = -20.949874371Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.050125629, -20.949874371}
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