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Simplifying -2.37x2 + 66.44x + 696.39 = 900 Reorder the terms: 696.39 + 66.44x + -2.37x2 = 900 Solving 696.39 + 66.44x + -2.37x2 = 900 Solving for variable 'x'. Reorder the terms: 696.39 + -900 + 66.44x + -2.37x2 = 900 + -900 Combine like terms: 696.39 + -900 = -203.61 -203.61 + 66.44x + -2.37x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -203.61 + 66.44x + -2.37x2 = 0 Begin completing the square. Divide all terms by -2.37 the coefficient of the squared term: Divide each side by '-2.37'. 85.91139241 + -28.03375527x + x2 = 0 Move the constant term to the right: Add '-85.91139241' to each side of the equation. 85.91139241 + -28.03375527x + -85.91139241 + x2 = 0 + -85.91139241 Reorder the terms: 85.91139241 + -85.91139241 + -28.03375527x + x2 = 0 + -85.91139241 Combine like terms: 85.91139241 + -85.91139241 = 0.00000000 0.00000000 + -28.03375527x + x2 = 0 + -85.91139241 -28.03375527x + x2 = 0 + -85.91139241 Combine like terms: 0 + -85.91139241 = -85.91139241 -28.03375527x + x2 = -85.91139241 The x term is -28.03375527x. Take half its coefficient (-14.01687764). Square it (196.4728588) and add it to both sides. Add '196.4728588' to each side of the equation. -28.03375527x + 196.4728588 + x2 = -85.91139241 + 196.4728588 Reorder the terms: 196.4728588 + -28.03375527x + x2 = -85.91139241 + 196.4728588 Combine like terms: -85.91139241 + 196.4728588 = 110.56146639 196.4728588 + -28.03375527x + x2 = 110.56146639 Factor a perfect square on the left side: (x + -14.01687764)(x + -14.01687764) = 110.56146639 Calculate the square root of the right side: 10.514821272 Break this problem into two subproblems by setting (x + -14.01687764) equal to 10.514821272 and -10.514821272.Subproblem 1
x + -14.01687764 = 10.514821272 Simplifying x + -14.01687764 = 10.514821272 Reorder the terms: -14.01687764 + x = 10.514821272 Solving -14.01687764 + x = 10.514821272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.01687764' to each side of the equation. -14.01687764 + 14.01687764 + x = 10.514821272 + 14.01687764 Combine like terms: -14.01687764 + 14.01687764 = 0.00000000 0.00000000 + x = 10.514821272 + 14.01687764 x = 10.514821272 + 14.01687764 Combine like terms: 10.514821272 + 14.01687764 = 24.531698912 x = 24.531698912 Simplifying x = 24.531698912Subproblem 2
x + -14.01687764 = -10.514821272 Simplifying x + -14.01687764 = -10.514821272 Reorder the terms: -14.01687764 + x = -10.514821272 Solving -14.01687764 + x = -10.514821272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.01687764' to each side of the equation. -14.01687764 + 14.01687764 + x = -10.514821272 + 14.01687764 Combine like terms: -14.01687764 + 14.01687764 = 0.00000000 0.00000000 + x = -10.514821272 + 14.01687764 x = -10.514821272 + 14.01687764 Combine like terms: -10.514821272 + 14.01687764 = 3.502056368 x = 3.502056368 Simplifying x = 3.502056368Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.531698912, 3.502056368}
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