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Simplifying 18x2 + -30x + -1 = 0 Reorder the terms: -1 + -30x + 18x2 = 0 Solving -1 + -30x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + -1.666666667x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + -1.666666667x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + -1.666666667x + x2 = 0 + 0.05555555556 -1.666666667x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 -1.666666667x + x2 = 0.05555555556 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 = 0.05555555556 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.05555555556 + 0.6944444447 Combine like terms: 0.05555555556 + 0.6944444447 = 0.75000000026 0.6944444447 + -1.666666667x + x2 = 0.75000000026 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.75000000026 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -0.8333333335 = 0.866025404 Simplifying x + -0.8333333335 = 0.866025404 Reorder the terms: -0.8333333335 + x = 0.866025404 Solving -0.8333333335 + x = 0.866025404 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 = 0.866025404 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.866025404 + 0.8333333335 x = 0.866025404 + 0.8333333335 Combine like terms: 0.866025404 + 0.8333333335 = 1.6993587375 x = 1.6993587375 Simplifying x = 1.6993587375Subproblem 2
x + -0.8333333335 = -0.866025404 Simplifying x + -0.8333333335 = -0.866025404 Reorder the terms: -0.8333333335 + x = -0.866025404 Solving -0.8333333335 + x = -0.866025404 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 = -0.866025404 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.866025404 + 0.8333333335 x = -0.866025404 + 0.8333333335 Combine like terms: -0.866025404 + 0.8333333335 = -0.0326920705 x = -0.0326920705 Simplifying x = -0.0326920705Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6993587375, -0.0326920705}
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