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Simplifying 2x2 + -585x + 1000 = 0 Reorder the terms: 1000 + -585x + 2x2 = 0 Solving 1000 + -585x + 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'. 500 + -292.5x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -292.5x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -292.5x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -292.5x + x2 = 0 + -500 -292.5x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -292.5x + x2 = -500 The x term is -292.5x. Take half its coefficient (-146.25). Square it (21389.0625) and add it to both sides. Add '21389.0625' to each side of the equation. -292.5x + 21389.0625 + x2 = -500 + 21389.0625 Reorder the terms: 21389.0625 + -292.5x + x2 = -500 + 21389.0625 Combine like terms: -500 + 21389.0625 = 20889.0625 21389.0625 + -292.5x + x2 = 20889.0625 Factor a perfect square on the left side: (x + -146.25)(x + -146.25) = 20889.0625 Calculate the square root of the right side: 144.530489863 Break this problem into two subproblems by setting (x + -146.25) equal to 144.530489863 and -144.530489863.Subproblem 1
x + -146.25 = 144.530489863 Simplifying x + -146.25 = 144.530489863 Reorder the terms: -146.25 + x = 144.530489863 Solving -146.25 + x = 144.530489863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '146.25' to each side of the equation. -146.25 + 146.25 + x = 144.530489863 + 146.25 Combine like terms: -146.25 + 146.25 = 0.00 0.00 + x = 144.530489863 + 146.25 x = 144.530489863 + 146.25 Combine like terms: 144.530489863 + 146.25 = 290.780489863 x = 290.780489863 Simplifying x = 290.780489863Subproblem 2
x + -146.25 = -144.530489863 Simplifying x + -146.25 = -144.530489863 Reorder the terms: -146.25 + x = -144.530489863 Solving -146.25 + x = -144.530489863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '146.25' to each side of the equation. -146.25 + 146.25 + x = -144.530489863 + 146.25 Combine like terms: -146.25 + 146.25 = 0.00 0.00 + x = -144.530489863 + 146.25 x = -144.530489863 + 146.25 Combine like terms: -144.530489863 + 146.25 = 1.719510137 x = 1.719510137 Simplifying x = 1.719510137Solution
The solution to the problem is based on the solutions from the subproblems. x = {290.780489863, 1.719510137}
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