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Simplifying m2 + 22m + -3 = 0 Reorder the terms: -3 + 22m + m2 = 0 Solving -3 + 22m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 22m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + 22m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 22m + m2 = 0 + 3 22m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 22m + m2 = 3 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 = 3 + 121 Reorder the terms: 121 + 22m + m2 = 3 + 121 Combine like terms: 3 + 121 = 124 121 + 22m + m2 = 124 Factor a perfect square on the left side: (m + 11)(m + 11) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (m + 11) equal to 11.135528726 and -11.135528726.Subproblem 1
m + 11 = 11.135528726 Simplifying m + 11 = 11.135528726 Reorder the terms: 11 + m = 11.135528726 Solving 11 + m = 11.135528726 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 = 11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + m = 11.135528726 + -11 m = 11.135528726 + -11 Combine like terms: 11.135528726 + -11 = 0.135528726 m = 0.135528726 Simplifying m = 0.135528726Subproblem 2
m + 11 = -11.135528726 Simplifying m + 11 = -11.135528726 Reorder the terms: 11 + m = -11.135528726 Solving 11 + m = -11.135528726 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 = -11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + m = -11.135528726 + -11 m = -11.135528726 + -11 Combine like terms: -11.135528726 + -11 = -22.135528726 m = -22.135528726 Simplifying m = -22.135528726Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.135528726, -22.135528726}
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