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Simplifying 0.01125x2 + -13.05x + 1800 = 0 Reorder the terms: 1800 + -13.05x + 0.01125x2 = 0 Solving 1800 + -13.05x + 0.01125x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01125 the coefficient of the squared term: Divide each side by '0.01125'. 160000 + -1160x + x2 = 0 Move the constant term to the right: Add '-160000' to each side of the equation. 160000 + -1160x + -160000 + x2 = 0 + -160000 Reorder the terms: 160000 + -160000 + -1160x + x2 = 0 + -160000 Combine like terms: 160000 + -160000 = 0 0 + -1160x + x2 = 0 + -160000 -1160x + x2 = 0 + -160000 Combine like terms: 0 + -160000 = -160000 -1160x + x2 = -160000 The x term is -1160x. Take half its coefficient (-580). Square it (336400) and add it to both sides. Add '336400' to each side of the equation. -1160x + 336400 + x2 = -160000 + 336400 Reorder the terms: 336400 + -1160x + x2 = -160000 + 336400 Combine like terms: -160000 + 336400 = 176400 336400 + -1160x + x2 = 176400 Factor a perfect square on the left side: (x + -580)(x + -580) = 176400 Calculate the square root of the right side: 420 Break this problem into two subproblems by setting (x + -580) equal to 420 and -420.Subproblem 1
x + -580 = 420 Simplifying x + -580 = 420 Reorder the terms: -580 + x = 420 Solving -580 + x = 420 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '580' to each side of the equation. -580 + 580 + x = 420 + 580 Combine like terms: -580 + 580 = 0 0 + x = 420 + 580 x = 420 + 580 Combine like terms: 420 + 580 = 1000 x = 1000 Simplifying x = 1000Subproblem 2
x + -580 = -420 Simplifying x + -580 = -420 Reorder the terms: -580 + x = -420 Solving -580 + x = -420 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '580' to each side of the equation. -580 + 580 + x = -420 + 580 Combine like terms: -580 + 580 = 0 0 + x = -420 + 580 x = -420 + 580 Combine like terms: -420 + 580 = 160 x = 160 Simplifying x = 160Solution
The solution to the problem is based on the solutions from the subproblems. x = {1000, 160}
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