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Simplifying 3x2 + -3x + 8x = 240 Reorder the terms: -3x + 8x + 3x2 = 240 Combine like terms: -3x + 8x = 5x 5x + 3x2 = 240 Solving 5x + 3x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 5x + 3x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -80 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 1.666666667x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 1.666666667x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 1.666666667x + x2 = 0 + 80 1.666666667x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 1.666666667x + x2 = 80 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 80 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 80 + 0.6944444447 Combine like terms: 80 + 0.6944444447 = 80.6944444447 0.6944444447 + 1.666666667x + x2 = 80.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 80.6944444447 Calculate the square root of the right side: 8.983008652 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 8.983008652 and -8.983008652.Subproblem 1
x + 0.8333333335 = 8.983008652 Simplifying x + 0.8333333335 = 8.983008652 Reorder the terms: 0.8333333335 + x = 8.983008652 Solving 0.8333333335 + x = 8.983008652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 8.983008652 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 8.983008652 + -0.8333333335 x = 8.983008652 + -0.8333333335 Combine like terms: 8.983008652 + -0.8333333335 = 8.1496753185 x = 8.1496753185 Simplifying x = 8.1496753185Subproblem 2
x + 0.8333333335 = -8.983008652 Simplifying x + 0.8333333335 = -8.983008652 Reorder the terms: 0.8333333335 + x = -8.983008652 Solving 0.8333333335 + x = -8.983008652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -8.983008652 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -8.983008652 + -0.8333333335 x = -8.983008652 + -0.8333333335 Combine like terms: -8.983008652 + -0.8333333335 = -9.8163419855 x = -9.8163419855 Simplifying x = -9.8163419855Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.1496753185, -9.8163419855}
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