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Simplifying -1x2 + 180x + -1800 = 0 Reorder the terms: -1800 + 180x + -1x2 = 0 Solving -1800 + 180x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1800 + -180x + x2 = 0 Move the constant term to the right: Add '-1800' to each side of the equation. 1800 + -180x + -1800 + x2 = 0 + -1800 Reorder the terms: 1800 + -1800 + -180x + x2 = 0 + -1800 Combine like terms: 1800 + -1800 = 0 0 + -180x + x2 = 0 + -1800 -180x + x2 = 0 + -1800 Combine like terms: 0 + -1800 = -1800 -180x + x2 = -1800 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -1800 + 8100 Reorder the terms: 8100 + -180x + x2 = -1800 + 8100 Combine like terms: -1800 + 8100 = 6300 8100 + -180x + x2 = 6300 Factor a perfect square on the left side: (x + -90)(x + -90) = 6300 Calculate the square root of the right side: 79.372539332 Break this problem into two subproblems by setting (x + -90) equal to 79.372539332 and -79.372539332.Subproblem 1
x + -90 = 79.372539332 Simplifying x + -90 = 79.372539332 Reorder the terms: -90 + x = 79.372539332 Solving -90 + x = 79.372539332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 79.372539332 + 90 Combine like terms: -90 + 90 = 0 0 + x = 79.372539332 + 90 x = 79.372539332 + 90 Combine like terms: 79.372539332 + 90 = 169.372539332 x = 169.372539332 Simplifying x = 169.372539332Subproblem 2
x + -90 = -79.372539332 Simplifying x + -90 = -79.372539332 Reorder the terms: -90 + x = -79.372539332 Solving -90 + x = -79.372539332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -79.372539332 + 90 Combine like terms: -90 + 90 = 0 0 + x = -79.372539332 + 90 x = -79.372539332 + 90 Combine like terms: -79.372539332 + 90 = 10.627460668 x = 10.627460668 Simplifying x = 10.627460668Solution
The solution to the problem is based on the solutions from the subproblems. x = {169.372539332, 10.627460668}
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