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Simplifying 3x2 + 5x + -40 = 0 Reorder the terms: -40 + 5x + 3x2 = 0 Solving -40 + 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'. -13.33333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + 1.666666667x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + 1.666666667x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + 1.666666667x + x2 = 0 + 13.33333333 1.666666667x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 1.666666667x + x2 = 13.33333333 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 = 13.33333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 13.33333333 + 0.6944444447 Combine like terms: 13.33333333 + 0.6944444447 = 14.0277777747 0.6944444447 + 1.666666667x + x2 = 14.0277777747 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 14.0277777747 Calculate the square root of the right side: 3.745367509 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.745367509 and -3.745367509.Subproblem 1
x + 0.8333333335 = 3.745367509 Simplifying x + 0.8333333335 = 3.745367509 Reorder the terms: 0.8333333335 + x = 3.745367509 Solving 0.8333333335 + x = 3.745367509 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 = 3.745367509 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.745367509 + -0.8333333335 x = 3.745367509 + -0.8333333335 Combine like terms: 3.745367509 + -0.8333333335 = 2.9120341755 x = 2.9120341755 Simplifying x = 2.9120341755Subproblem 2
x + 0.8333333335 = -3.745367509 Simplifying x + 0.8333333335 = -3.745367509 Reorder the terms: 0.8333333335 + x = -3.745367509 Solving 0.8333333335 + x = -3.745367509 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 = -3.745367509 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.745367509 + -0.8333333335 x = -3.745367509 + -0.8333333335 Combine like terms: -3.745367509 + -0.8333333335 = -4.5787008425 x = -4.5787008425 Simplifying x = -4.5787008425Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9120341755, -4.5787008425}
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