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Simplifying m2 + 22m = 17 Reorder the terms: 22m + m2 = 17 Solving 22m + m2 = 17 Solving for variable 'm'. Reorder the terms: -17 + 22m + m2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 22m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 22m + 17 + m2 = 0 + 17 Reorder the terms: -17 + 17 + 22m + m2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 22m + m2 = 0 + 17 22m + m2 = 0 + 17 Combine like terms: 0 + 17 = 17 22m + m2 = 17 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 = 17 + 121 Reorder the terms: 121 + 22m + m2 = 17 + 121 Combine like terms: 17 + 121 = 138 121 + 22m + m2 = 138 Factor a perfect square on the left side: (m + 11)(m + 11) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (m + 11) equal to 11.747340124 and -11.747340124.Subproblem 1
m + 11 = 11.747340124 Simplifying m + 11 = 11.747340124 Reorder the terms: 11 + m = 11.747340124 Solving 11 + m = 11.747340124 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 = 11.747340124 + -11 Combine like terms: 11 + -11 = 0 0 + m = 11.747340124 + -11 m = 11.747340124 + -11 Combine like terms: 11.747340124 + -11 = 0.747340124 m = 0.747340124 Simplifying m = 0.747340124Subproblem 2
m + 11 = -11.747340124 Simplifying m + 11 = -11.747340124 Reorder the terms: 11 + m = -11.747340124 Solving 11 + m = -11.747340124 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 = -11.747340124 + -11 Combine like terms: 11 + -11 = 0 0 + m = -11.747340124 + -11 m = -11.747340124 + -11 Combine like terms: -11.747340124 + -11 = -22.747340124 m = -22.747340124 Simplifying m = -22.747340124Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.747340124, -22.747340124}
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