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Simplifying 2x2 + -155x + 1800 = 0 Reorder the terms: 1800 + -155x + 2x2 = 0 Solving 1800 + -155x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 900 + -77.5x + x2 = 0 Move the constant term to the right: Add '-900' to each side of the equation. 900 + -77.5x + -900 + x2 = 0 + -900 Reorder the terms: 900 + -900 + -77.5x + x2 = 0 + -900 Combine like terms: 900 + -900 = 0 0 + -77.5x + x2 = 0 + -900 -77.5x + x2 = 0 + -900 Combine like terms: 0 + -900 = -900 -77.5x + x2 = -900 The x term is -77.5x. Take half its coefficient (-38.75). Square it (1501.5625) and add it to both sides. Add '1501.5625' to each side of the equation. -77.5x + 1501.5625 + x2 = -900 + 1501.5625 Reorder the terms: 1501.5625 + -77.5x + x2 = -900 + 1501.5625 Combine like terms: -900 + 1501.5625 = 601.5625 1501.5625 + -77.5x + x2 = 601.5625 Factor a perfect square on the left side: (x + -38.75)(x + -38.75) = 601.5625 Calculate the square root of the right side: 24.526771088 Break this problem into two subproblems by setting (x + -38.75) equal to 24.526771088 and -24.526771088.Subproblem 1
x + -38.75 = 24.526771088 Simplifying x + -38.75 = 24.526771088 Reorder the terms: -38.75 + x = 24.526771088 Solving -38.75 + x = 24.526771088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.75' to each side of the equation. -38.75 + 38.75 + x = 24.526771088 + 38.75 Combine like terms: -38.75 + 38.75 = 0.00 0.00 + x = 24.526771088 + 38.75 x = 24.526771088 + 38.75 Combine like terms: 24.526771088 + 38.75 = 63.276771088 x = 63.276771088 Simplifying x = 63.276771088Subproblem 2
x + -38.75 = -24.526771088 Simplifying x + -38.75 = -24.526771088 Reorder the terms: -38.75 + x = -24.526771088 Solving -38.75 + x = -24.526771088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.75' to each side of the equation. -38.75 + 38.75 + x = -24.526771088 + 38.75 Combine like terms: -38.75 + 38.75 = 0.00 0.00 + x = -24.526771088 + 38.75 x = -24.526771088 + 38.75 Combine like terms: -24.526771088 + 38.75 = 14.223228912 x = 14.223228912 Simplifying x = 14.223228912Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.276771088, 14.223228912}
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