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Simplifying m2 + 4m + -27 = 6 Reorder the terms: -27 + 4m + m2 = 6 Solving -27 + 4m + m2 = 6 Solving for variable 'm'. Reorder the terms: -27 + -6 + 4m + m2 = 6 + -6 Combine like terms: -27 + -6 = -33 -33 + 4m + m2 = 6 + -6 Combine like terms: 6 + -6 = 0 -33 + 4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 4m + 33 + m2 = 0 + 33 Reorder the terms: -33 + 33 + 4m + m2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4m + m2 = 0 + 33 4m + m2 = 0 + 33 Combine like terms: 0 + 33 = 33 4m + m2 = 33 The m term is 4m. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m + 4 + m2 = 33 + 4 Reorder the terms: 4 + 4m + m2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + 4m + m2 = 37 Factor a perfect square on the left side: (m + 2)(m + 2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (m + 2) equal to 6.08276253 and -6.08276253.Subproblem 1
m + 2 = 6.08276253 Simplifying m + 2 = 6.08276253 Reorder the terms: 2 + m = 6.08276253 Solving 2 + m = 6.08276253 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + m = 6.08276253 + -2 m = 6.08276253 + -2 Combine like terms: 6.08276253 + -2 = 4.08276253 m = 4.08276253 Simplifying m = 4.08276253Subproblem 2
m + 2 = -6.08276253 Simplifying m + 2 = -6.08276253 Reorder the terms: 2 + m = -6.08276253 Solving 2 + m = -6.08276253 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = -6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + m = -6.08276253 + -2 m = -6.08276253 + -2 Combine like terms: -6.08276253 + -2 = -8.08276253 m = -8.08276253 Simplifying m = -8.08276253Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.08276253, -8.08276253}
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