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Simplifying 3x2 + 5x + -120 = 0 Reorder the terms: -120 + 5x + 3x2 = 0 Solving -120 + 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'. -40 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 1.666666667x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 1.666666667x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 1.666666667x + x2 = 0 + 40 1.666666667x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 1.666666667x + x2 = 40 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 = 40 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 40 + 0.6944444447 Combine like terms: 40 + 0.6944444447 = 40.6944444447 0.6944444447 + 1.666666667x + x2 = 40.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 40.6944444447 Calculate the square root of the right side: 6.379219736 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 6.379219736 and -6.379219736.Subproblem 1
x + 0.8333333335 = 6.379219736 Simplifying x + 0.8333333335 = 6.379219736 Reorder the terms: 0.8333333335 + x = 6.379219736 Solving 0.8333333335 + x = 6.379219736 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 = 6.379219736 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 6.379219736 + -0.8333333335 x = 6.379219736 + -0.8333333335 Combine like terms: 6.379219736 + -0.8333333335 = 5.5458864025 x = 5.5458864025 Simplifying x = 5.5458864025Subproblem 2
x + 0.8333333335 = -6.379219736 Simplifying x + 0.8333333335 = -6.379219736 Reorder the terms: 0.8333333335 + x = -6.379219736 Solving 0.8333333335 + x = -6.379219736 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 = -6.379219736 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -6.379219736 + -0.8333333335 x = -6.379219736 + -0.8333333335 Combine like terms: -6.379219736 + -0.8333333335 = -7.2125530695 x = -7.2125530695 Simplifying x = -7.2125530695Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5458864025, -7.2125530695}
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