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Simplifying m2 + 4m + -17 = -3 Reorder the terms: -17 + 4m + m2 = -3 Solving -17 + 4m + m2 = -3 Solving for variable 'm'. Reorder the terms: -17 + 3 + 4m + m2 = -3 + 3 Combine like terms: -17 + 3 = -14 -14 + 4m + m2 = -3 + 3 Combine like terms: -3 + 3 = 0 -14 + 4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 4m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + 4m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 4m + m2 = 0 + 14 4m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 4m + m2 = 14 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 = 14 + 4 Reorder the terms: 4 + 4m + m2 = 14 + 4 Combine like terms: 14 + 4 = 18 4 + 4m + m2 = 18 Factor a perfect square on the left side: (m + 2)(m + 2) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (m + 2) equal to 4.242640687 and -4.242640687.Subproblem 1
m + 2 = 4.242640687 Simplifying m + 2 = 4.242640687 Reorder the terms: 2 + m = 4.242640687 Solving 2 + m = 4.242640687 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 = 4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + m = 4.242640687 + -2 m = 4.242640687 + -2 Combine like terms: 4.242640687 + -2 = 2.242640687 m = 2.242640687 Simplifying m = 2.242640687Subproblem 2
m + 2 = -4.242640687 Simplifying m + 2 = -4.242640687 Reorder the terms: 2 + m = -4.242640687 Solving 2 + m = -4.242640687 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 = -4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + m = -4.242640687 + -2 m = -4.242640687 + -2 Combine like terms: -4.242640687 + -2 = -6.242640687 m = -6.242640687 Simplifying m = -6.242640687Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.242640687, -6.242640687}
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