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Simplifying 3x2 + -5x + -240 = 0 Reorder the terms: -240 + -5x + 3x2 = 0 Solving -240 + -5x + 3x2 = 0 Solving for variable 'x'. 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 = 9.8163419855 x = 9.8163419855 Simplifying x = 9.8163419855Subproblem 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 = -8.1496753185 x = -8.1496753185 Simplifying x = -8.1496753185Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.8163419855, -8.1496753185}
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