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Simplifying m2 + 1 = 22m Reorder the terms: 1 + m2 = 22m Solving 1 + m2 = 22m Solving for variable 'm'. Reorder the terms: 1 + -22m + m2 = 22m + -22m Combine like terms: 22m + -22m = 0 1 + -22m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -22m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -22m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -22m + m2 = 0 + -1 -22m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -22m + m2 = -1 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 = -1 + 121 Reorder the terms: 121 + -22m + m2 = -1 + 121 Combine like terms: -1 + 121 = 120 121 + -22m + m2 = 120 Factor a perfect square on the left side: (m + -11)(m + -11) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (m + -11) equal to 10.95445115 and -10.95445115.Subproblem 1
m + -11 = 10.95445115 Simplifying m + -11 = 10.95445115 Reorder the terms: -11 + m = 10.95445115 Solving -11 + m = 10.95445115 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 = 10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + m = 10.95445115 + 11 m = 10.95445115 + 11 Combine like terms: 10.95445115 + 11 = 21.95445115 m = 21.95445115 Simplifying m = 21.95445115Subproblem 2
m + -11 = -10.95445115 Simplifying m + -11 = -10.95445115 Reorder the terms: -11 + m = -10.95445115 Solving -11 + m = -10.95445115 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 = -10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + m = -10.95445115 + 11 m = -10.95445115 + 11 Combine like terms: -10.95445115 + 11 = 0.04554885 m = 0.04554885 Simplifying m = 0.04554885Solution
The solution to the problem is based on the solutions from the subproblems. m = {21.95445115, 0.04554885}
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