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Simplifying m2 + 22m + -7 = 0 Reorder the terms: -7 + 22m + m2 = 0 Solving -7 + 22m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 22m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + 22m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 22m + m2 = 0 + 7 22m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 22m + m2 = 7 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 = 7 + 121 Reorder the terms: 121 + 22m + m2 = 7 + 121 Combine like terms: 7 + 121 = 128 121 + 22m + m2 = 128 Factor a perfect square on the left side: (m + 11)(m + 11) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (m + 11) equal to 11.313708499 and -11.313708499.Subproblem 1
m + 11 = 11.313708499 Simplifying m + 11 = 11.313708499 Reorder the terms: 11 + m = 11.313708499 Solving 11 + m = 11.313708499 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 = 11.313708499 + -11 Combine like terms: 11 + -11 = 0 0 + m = 11.313708499 + -11 m = 11.313708499 + -11 Combine like terms: 11.313708499 + -11 = 0.313708499 m = 0.313708499 Simplifying m = 0.313708499Subproblem 2
m + 11 = -11.313708499 Simplifying m + 11 = -11.313708499 Reorder the terms: 11 + m = -11.313708499 Solving 11 + m = -11.313708499 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 = -11.313708499 + -11 Combine like terms: 11 + -11 = 0 0 + m = -11.313708499 + -11 m = -11.313708499 + -11 Combine like terms: -11.313708499 + -11 = -22.313708499 m = -22.313708499 Simplifying m = -22.313708499Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.313708499, -22.313708499}
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