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Simplifying m2 + 4m + -27 = 3 Reorder the terms: -27 + 4m + m2 = 3 Solving -27 + 4m + m2 = 3 Solving for variable 'm'. Reorder the terms: -27 + -3 + 4m + m2 = 3 + -3 Combine like terms: -27 + -3 = -30 -30 + 4m + m2 = 3 + -3 Combine like terms: 3 + -3 = 0 -30 + 4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 4m + 30 + m2 = 0 + 30 Reorder the terms: -30 + 30 + 4m + m2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 4m + m2 = 0 + 30 4m + m2 = 0 + 30 Combine like terms: 0 + 30 = 30 4m + m2 = 30 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 = 30 + 4 Reorder the terms: 4 + 4m + m2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + 4m + m2 = 34 Factor a perfect square on the left side: (m + 2)(m + 2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (m + 2) equal to 5.830951895 and -5.830951895.Subproblem 1
m + 2 = 5.830951895 Simplifying m + 2 = 5.830951895 Reorder the terms: 2 + m = 5.830951895 Solving 2 + m = 5.830951895 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 = 5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + m = 5.830951895 + -2 m = 5.830951895 + -2 Combine like terms: 5.830951895 + -2 = 3.830951895 m = 3.830951895 Simplifying m = 3.830951895Subproblem 2
m + 2 = -5.830951895 Simplifying m + 2 = -5.830951895 Reorder the terms: 2 + m = -5.830951895 Solving 2 + m = -5.830951895 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 = -5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + m = -5.830951895 + -2 m = -5.830951895 + -2 Combine like terms: -5.830951895 + -2 = -7.830951895 m = -7.830951895 Simplifying m = -7.830951895Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.830951895, -7.830951895}
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