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Simplifying (-2x + 700)(x + 20) + -1(-1x2 + 700) = 0 Reorder the terms: (700 + -2x)(x + 20) + -1(-1x2 + 700) = 0 Reorder the terms: (700 + -2x)(20 + x) + -1(-1x2 + 700) = 0 Multiply (700 + -2x) * (20 + x) (700(20 + x) + -2x * (20 + x)) + -1(-1x2 + 700) = 0 ((20 * 700 + x * 700) + -2x * (20 + x)) + -1(-1x2 + 700) = 0 ((14000 + 700x) + -2x * (20 + x)) + -1(-1x2 + 700) = 0 (14000 + 700x + (20 * -2x + x * -2x)) + -1(-1x2 + 700) = 0 (14000 + 700x + (-40x + -2x2)) + -1(-1x2 + 700) = 0 Combine like terms: 700x + -40x = 660x (14000 + 660x + -2x2) + -1(-1x2 + 700) = 0 Reorder the terms: 14000 + 660x + -2x2 + -1(700 + -1x2) = 0 14000 + 660x + -2x2 + (700 * -1 + -1x2 * -1) = 0 14000 + 660x + -2x2 + (-700 + 1x2) = 0 Reorder the terms: 14000 + -700 + 660x + -2x2 + 1x2 = 0 Combine like terms: 14000 + -700 = 13300 13300 + 660x + -2x2 + 1x2 = 0 Combine like terms: -2x2 + 1x2 = -1x2 13300 + 660x + -1x2 = 0 Solving 13300 + 660x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13300 + -660x + x2 = 0 Move the constant term to the right: Add '13300' to each side of the equation. -13300 + -660x + 13300 + x2 = 0 + 13300 Reorder the terms: -13300 + 13300 + -660x + x2 = 0 + 13300 Combine like terms: -13300 + 13300 = 0 0 + -660x + x2 = 0 + 13300 -660x + x2 = 0 + 13300 Combine like terms: 0 + 13300 = 13300 -660x + x2 = 13300 The x term is -660x. Take half its coefficient (-330). Square it (108900) and add it to both sides. Add '108900' to each side of the equation. -660x + 108900 + x2 = 13300 + 108900 Reorder the terms: 108900 + -660x + x2 = 13300 + 108900 Combine like terms: 13300 + 108900 = 122200 108900 + -660x + x2 = 122200 Factor a perfect square on the left side: (x + -330)(x + -330) = 122200 Calculate the square root of the right side: 349.571165859 Break this problem into two subproblems by setting (x + -330) equal to 349.571165859 and -349.571165859.Subproblem 1
x + -330 = 349.571165859 Simplifying x + -330 = 349.571165859 Reorder the terms: -330 + x = 349.571165859 Solving -330 + x = 349.571165859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '330' to each side of the equation. -330 + 330 + x = 349.571165859 + 330 Combine like terms: -330 + 330 = 0 0 + x = 349.571165859 + 330 x = 349.571165859 + 330 Combine like terms: 349.571165859 + 330 = 679.571165859 x = 679.571165859 Simplifying x = 679.571165859Subproblem 2
x + -330 = -349.571165859 Simplifying x + -330 = -349.571165859 Reorder the terms: -330 + x = -349.571165859 Solving -330 + x = -349.571165859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '330' to each side of the equation. -330 + 330 + x = -349.571165859 + 330 Combine like terms: -330 + 330 = 0 0 + x = -349.571165859 + 330 x = -349.571165859 + 330 Combine like terms: -349.571165859 + 330 = -19.571165859 x = -19.571165859 Simplifying x = -19.571165859Solution
The solution to the problem is based on the solutions from the subproblems. x = {679.571165859, -19.571165859}
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