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Simplifying (x2) + 3x = 240 x2 + 3x = 240 Reorder the terms: 3x + x2 = 240 Solving 3x + x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 3x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 3x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 3x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 3x + x2 = 0 + 240 3x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 3x + x2 = 240 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 = 240 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 240 + 2.25 Combine like terms: 240 + 2.25 = 242.25 2.25 + 3x + x2 = 242.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 242.25 Calculate the square root of the right side: 15.564382416 Break this problem into two subproblems by setting (x + 1.5) equal to 15.564382416 and -15.564382416.Subproblem 1
x + 1.5 = 15.564382416 Simplifying x + 1.5 = 15.564382416 Reorder the terms: 1.5 + x = 15.564382416 Solving 1.5 + x = 15.564382416 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 = 15.564382416 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.564382416 + -1.5 x = 15.564382416 + -1.5 Combine like terms: 15.564382416 + -1.5 = 14.064382416 x = 14.064382416 Simplifying x = 14.064382416Subproblem 2
x + 1.5 = -15.564382416 Simplifying x + 1.5 = -15.564382416 Reorder the terms: 1.5 + x = -15.564382416 Solving 1.5 + x = -15.564382416 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 = -15.564382416 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.564382416 + -1.5 x = -15.564382416 + -1.5 Combine like terms: -15.564382416 + -1.5 = -17.064382416 x = -17.064382416 Simplifying x = -17.064382416Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.064382416, -17.064382416}
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