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Simplifying 2x2 + -2015x + 2015 = 0 Reorder the terms: 2015 + -2015x + 2x2 = 0 Solving 2015 + -2015x + 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'. 1007.5 + -1007.5x + x2 = 0 Move the constant term to the right: Add '-1007.5' to each side of the equation. 1007.5 + -1007.5x + -1007.5 + x2 = 0 + -1007.5 Reorder the terms: 1007.5 + -1007.5 + -1007.5x + x2 = 0 + -1007.5 Combine like terms: 1007.5 + -1007.5 = 0.0 0.0 + -1007.5x + x2 = 0 + -1007.5 -1007.5x + x2 = 0 + -1007.5 Combine like terms: 0 + -1007.5 = -1007.5 -1007.5x + x2 = -1007.5 The x term is -1007.5x. Take half its coefficient (-503.75). Square it (253764.0625) and add it to both sides. Add '253764.0625' to each side of the equation. -1007.5x + 253764.0625 + x2 = -1007.5 + 253764.0625 Reorder the terms: 253764.0625 + -1007.5x + x2 = -1007.5 + 253764.0625 Combine like terms: -1007.5 + 253764.0625 = 252756.5625 253764.0625 + -1007.5x + x2 = 252756.5625 Factor a perfect square on the left side: (x + -503.75)(x + -503.75) = 252756.5625 Calculate the square root of the right side: 502.749005469 Break this problem into two subproblems by setting (x + -503.75) equal to 502.749005469 and -502.749005469.Subproblem 1
x + -503.75 = 502.749005469 Simplifying x + -503.75 = 502.749005469 Reorder the terms: -503.75 + x = 502.749005469 Solving -503.75 + x = 502.749005469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '503.75' to each side of the equation. -503.75 + 503.75 + x = 502.749005469 + 503.75 Combine like terms: -503.75 + 503.75 = 0.00 0.00 + x = 502.749005469 + 503.75 x = 502.749005469 + 503.75 Combine like terms: 502.749005469 + 503.75 = 1006.499005469 x = 1006.499005469 Simplifying x = 1006.499005469Subproblem 2
x + -503.75 = -502.749005469 Simplifying x + -503.75 = -502.749005469 Reorder the terms: -503.75 + x = -502.749005469 Solving -503.75 + x = -502.749005469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '503.75' to each side of the equation. -503.75 + 503.75 + x = -502.749005469 + 503.75 Combine like terms: -503.75 + 503.75 = 0.00 0.00 + x = -502.749005469 + 503.75 x = -502.749005469 + 503.75 Combine like terms: -502.749005469 + 503.75 = 1.000994531 x = 1.000994531 Simplifying x = 1.000994531Solution
The solution to the problem is based on the solutions from the subproblems. x = {1006.499005469, 1.000994531}
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