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Simplifying x = 3x(90 + -1x) + 18 x = (90 * 3x + -1x * 3x) + 18 x = (270x + -3x2) + 18 Reorder the terms: x = 18 + 270x + -3x2 Solving x = 18 + 270x + -3x2 Solving for variable 'x'. Reorder the terms: -18 + x + -270x + 3x2 = 18 + 270x + -3x2 + -18 + -270x + 3x2 Combine like terms: x + -270x = -269x -18 + -269x + 3x2 = 18 + 270x + -3x2 + -18 + -270x + 3x2 Reorder the terms: -18 + -269x + 3x2 = 18 + -18 + 270x + -270x + -3x2 + 3x2 Combine like terms: 18 + -18 = 0 -18 + -269x + 3x2 = 0 + 270x + -270x + -3x2 + 3x2 -18 + -269x + 3x2 = 270x + -270x + -3x2 + 3x2 Combine like terms: 270x + -270x = 0 -18 + -269x + 3x2 = 0 + -3x2 + 3x2 -18 + -269x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -18 + -269x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -89.66666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -89.66666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -89.66666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -89.66666667x + x2 = 0 + 6 -89.66666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -89.66666667x + x2 = 6 The x term is -89.66666667x. Take half its coefficient (-44.83333334). Square it (2010.027778) and add it to both sides. Add '2010.027778' to each side of the equation. -89.66666667x + 2010.027778 + x2 = 6 + 2010.027778 Reorder the terms: 2010.027778 + -89.66666667x + x2 = 6 + 2010.027778 Combine like terms: 6 + 2010.027778 = 2016.027778 2010.027778 + -89.66666667x + x2 = 2016.027778 Factor a perfect square on the left side: (x + -44.83333334)(x + -44.83333334) = 2016.027778 Calculate the square root of the right side: 44.900197973 Break this problem into two subproblems by setting (x + -44.83333334) equal to 44.900197973 and -44.900197973.Subproblem 1
x + -44.83333334 = 44.900197973 Simplifying x + -44.83333334 = 44.900197973 Reorder the terms: -44.83333334 + x = 44.900197973 Solving -44.83333334 + x = 44.900197973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.83333334' to each side of the equation. -44.83333334 + 44.83333334 + x = 44.900197973 + 44.83333334 Combine like terms: -44.83333334 + 44.83333334 = 0.00000000 0.00000000 + x = 44.900197973 + 44.83333334 x = 44.900197973 + 44.83333334 Combine like terms: 44.900197973 + 44.83333334 = 89.733531313 x = 89.733531313 Simplifying x = 89.733531313Subproblem 2
x + -44.83333334 = -44.900197973 Simplifying x + -44.83333334 = -44.900197973 Reorder the terms: -44.83333334 + x = -44.900197973 Solving -44.83333334 + x = -44.900197973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.83333334' to each side of the equation. -44.83333334 + 44.83333334 + x = -44.900197973 + 44.83333334 Combine like terms: -44.83333334 + 44.83333334 = 0.00000000 0.00000000 + x = -44.900197973 + 44.83333334 x = -44.900197973 + 44.83333334 Combine like terms: -44.900197973 + 44.83333334 = -0.066864633 x = -0.066864633 Simplifying x = -0.066864633Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.733531313, -0.066864633}
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