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Simplifying 1012539.0625 = -4(x2) + 4025x Reorder the terms: 1012539.0625 = 4025x + -4x2 Solving 1012539.0625 = 4025x + -4x2 Solving for variable 'x'. Reorder the terms: 1012539.0625 + -4025x + 4x2 = 4025x + -4025x + -4x2 + 4x2 Combine like terms: 4025x + -4025x = 0 1012539.0625 + -4025x + 4x2 = 0 + -4x2 + 4x2 1012539.0625 + -4025x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 1012539.0625 + -4025x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 253134.7656 + -1006.25x + x2 = 0 Move the constant term to the right: Add '-253134.7656' to each side of the equation. 253134.7656 + -1006.25x + -253134.7656 + x2 = 0 + -253134.7656 Reorder the terms: 253134.7656 + -253134.7656 + -1006.25x + x2 = 0 + -253134.7656 Combine like terms: 253134.7656 + -253134.7656 = 0.0000 0.0000 + -1006.25x + x2 = 0 + -253134.7656 -1006.25x + x2 = 0 + -253134.7656 Combine like terms: 0 + -253134.7656 = -253134.7656 -1006.25x + x2 = -253134.7656 The x term is -1006.25x. Take half its coefficient (-503.125). Square it (253134.7656) and add it to both sides. Add '253134.7656' to each side of the equation. -1006.25x + 253134.7656 + x2 = -253134.7656 + 253134.7656 Reorder the terms: 253134.7656 + -1006.25x + x2 = -253134.7656 + 253134.7656 Combine like terms: -253134.7656 + 253134.7656 = 0.0000 253134.7656 + -1006.25x + x2 = 0.0000 Factor a perfect square on the left side: (x + -503.125)(x + -503.125) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -503.125) equal to 0.0000 and 0.0000.Subproblem 1
x + -503.125 = 0.0000 Simplifying x + -503.125 = 0.0000 Reorder the terms: -503.125 + x = 0.0000 Solving -503.125 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '503.125' to each side of the equation. -503.125 + 503.125 + x = 0.0000 + 503.125 Combine like terms: -503.125 + 503.125 = 0.000 0.000 + x = 0.0000 + 503.125 x = 0.0000 + 503.125 Combine like terms: 0.0000 + 503.125 = 503.125 x = 503.125 Simplifying x = 503.125Subproblem 2
x + -503.125 = 0.0000 Simplifying x + -503.125 = 0.0000 Reorder the terms: -503.125 + x = 0.0000 Solving -503.125 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '503.125' to each side of the equation. -503.125 + 503.125 + x = 0.0000 + 503.125 Combine like terms: -503.125 + 503.125 = 0.000 0.000 + x = 0.0000 + 503.125 x = 0.0000 + 503.125 Combine like terms: 0.0000 + 503.125 = 503.125 x = 503.125 Simplifying x = 503.125Solution
The solution to the problem is based on the solutions from the subproblems. x = {503.125, 503.125}
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