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Simplifying x(x + 3) = 252 Reorder the terms: x(3 + x) = 252 (3 * x + x * x) = 252 (3x + x2) = 252 Solving 3x + x2 = 252 Solving for variable 'x'. Reorder the terms: -252 + 3x + x2 = 252 + -252 Combine like terms: 252 + -252 = 0 -252 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '252' to each side of the equation. -252 + 3x + 252 + x2 = 0 + 252 Reorder the terms: -252 + 252 + 3x + x2 = 0 + 252 Combine like terms: -252 + 252 = 0 0 + 3x + x2 = 0 + 252 3x + x2 = 0 + 252 Combine like terms: 0 + 252 = 252 3x + x2 = 252 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 252 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 252 + 2.25 Combine like terms: 252 + 2.25 = 254.25 2.25 + 3x + x2 = 254.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 254.25 Calculate the square root of the right side: 15.945218719 Break this problem into two subproblems by setting (x + 1.5) equal to 15.945218719 and -15.945218719.Subproblem 1
x + 1.5 = 15.945218719 Simplifying x + 1.5 = 15.945218719 Reorder the terms: 1.5 + x = 15.945218719 Solving 1.5 + x = 15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 15.945218719 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.945218719 + -1.5 x = 15.945218719 + -1.5 Combine like terms: 15.945218719 + -1.5 = 14.445218719 x = 14.445218719 Simplifying x = 14.445218719Subproblem 2
x + 1.5 = -15.945218719 Simplifying x + 1.5 = -15.945218719 Reorder the terms: 1.5 + x = -15.945218719 Solving 1.5 + x = -15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -15.945218719 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.945218719 + -1.5 x = -15.945218719 + -1.5 Combine like terms: -15.945218719 + -1.5 = -17.445218719 x = -17.445218719 Simplifying x = -17.445218719Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.445218719, -17.445218719}
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