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Simplifying x2 + 3x = 459 Reorder the terms: 3x + x2 = 459 Solving 3x + x2 = 459 Solving for variable 'x'. Reorder the terms: -459 + 3x + x2 = 459 + -459 Combine like terms: 459 + -459 = 0 -459 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '459' to each side of the equation. -459 + 3x + 459 + x2 = 0 + 459 Reorder the terms: -459 + 459 + 3x + x2 = 0 + 459 Combine like terms: -459 + 459 = 0 0 + 3x + x2 = 0 + 459 3x + x2 = 0 + 459 Combine like terms: 0 + 459 = 459 3x + x2 = 459 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 = 459 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 459 + 2.25 Combine like terms: 459 + 2.25 = 461.25 2.25 + 3x + x2 = 461.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 461.25 Calculate the square root of the right side: 21.476731595 Break this problem into two subproblems by setting (x + 1.5) equal to 21.476731595 and -21.476731595.Subproblem 1
x + 1.5 = 21.476731595 Simplifying x + 1.5 = 21.476731595 Reorder the terms: 1.5 + x = 21.476731595 Solving 1.5 + x = 21.476731595 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 = 21.476731595 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 21.476731595 + -1.5 x = 21.476731595 + -1.5 Combine like terms: 21.476731595 + -1.5 = 19.976731595 x = 19.976731595 Simplifying x = 19.976731595Subproblem 2
x + 1.5 = -21.476731595 Simplifying x + 1.5 = -21.476731595 Reorder the terms: 1.5 + x = -21.476731595 Solving 1.5 + x = -21.476731595 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 = -21.476731595 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -21.476731595 + -1.5 x = -21.476731595 + -1.5 Combine like terms: -21.476731595 + -1.5 = -22.976731595 x = -22.976731595 Simplifying x = -22.976731595Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.976731595, -22.976731595}
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