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Simplifying 3x2 + 5x + -390 = 0 Reorder the terms: -390 + 5x + 3x2 = 0 Solving -390 + 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'. -130 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 1.666666667x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 1.666666667x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 1.666666667x + x2 = 0 + 130 1.666666667x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 1.666666667x + x2 = 130 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 = 130 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 130 + 0.6944444447 Combine like terms: 130 + 0.6944444447 = 130.6944444447 0.6944444447 + 1.666666667x + x2 = 130.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 130.6944444447 Calculate the square root of the right side: 11.432167093 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 11.432167093 and -11.432167093.Subproblem 1
x + 0.8333333335 = 11.432167093 Simplifying x + 0.8333333335 = 11.432167093 Reorder the terms: 0.8333333335 + x = 11.432167093 Solving 0.8333333335 + x = 11.432167093 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 = 11.432167093 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 11.432167093 + -0.8333333335 x = 11.432167093 + -0.8333333335 Combine like terms: 11.432167093 + -0.8333333335 = 10.5988337595 x = 10.5988337595 Simplifying x = 10.5988337595Subproblem 2
x + 0.8333333335 = -11.432167093 Simplifying x + 0.8333333335 = -11.432167093 Reorder the terms: 0.8333333335 + x = -11.432167093 Solving 0.8333333335 + x = -11.432167093 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 = -11.432167093 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -11.432167093 + -0.8333333335 x = -11.432167093 + -0.8333333335 Combine like terms: -11.432167093 + -0.8333333335 = -12.2655004265 x = -12.2655004265 Simplifying x = -12.2655004265Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.5988337595, -12.2655004265}
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