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Simplifying 3000 = 4x2 + -89x + 501 Reorder the terms: 3000 = 501 + -89x + 4x2 Solving 3000 = 501 + -89x + 4x2 Solving for variable 'x'. Combine like terms: 3000 + -501 = 2499 2499 + 89x + -4x2 = 501 + -89x + 4x2 + -501 + 89x + -4x2 Reorder the terms: 2499 + 89x + -4x2 = 501 + -501 + -89x + 89x + 4x2 + -4x2 Combine like terms: 501 + -501 = 0 2499 + 89x + -4x2 = 0 + -89x + 89x + 4x2 + -4x2 2499 + 89x + -4x2 = -89x + 89x + 4x2 + -4x2 Combine like terms: -89x + 89x = 0 2499 + 89x + -4x2 = 0 + 4x2 + -4x2 2499 + 89x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2499 + 89x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -624.75 + -22.25x + x2 = 0 Move the constant term to the right: Add '624.75' to each side of the equation. -624.75 + -22.25x + 624.75 + x2 = 0 + 624.75 Reorder the terms: -624.75 + 624.75 + -22.25x + x2 = 0 + 624.75 Combine like terms: -624.75 + 624.75 = 0.00 0.00 + -22.25x + x2 = 0 + 624.75 -22.25x + x2 = 0 + 624.75 Combine like terms: 0 + 624.75 = 624.75 -22.25x + x2 = 624.75 The x term is -22.25x. Take half its coefficient (-11.125). Square it (123.765625) and add it to both sides. Add '123.765625' to each side of the equation. -22.25x + 123.765625 + x2 = 624.75 + 123.765625 Reorder the terms: 123.765625 + -22.25x + x2 = 624.75 + 123.765625 Combine like terms: 624.75 + 123.765625 = 748.515625 123.765625 + -22.25x + x2 = 748.515625 Factor a perfect square on the left side: (x + -11.125)(x + -11.125) = 748.515625 Calculate the square root of the right side: 27.359013597 Break this problem into two subproblems by setting (x + -11.125) equal to 27.359013597 and -27.359013597.Subproblem 1
x + -11.125 = 27.359013597 Simplifying x + -11.125 = 27.359013597 Reorder the terms: -11.125 + x = 27.359013597 Solving -11.125 + x = 27.359013597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = 27.359013597 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = 27.359013597 + 11.125 x = 27.359013597 + 11.125 Combine like terms: 27.359013597 + 11.125 = 38.484013597 x = 38.484013597 Simplifying x = 38.484013597Subproblem 2
x + -11.125 = -27.359013597 Simplifying x + -11.125 = -27.359013597 Reorder the terms: -11.125 + x = -27.359013597 Solving -11.125 + x = -27.359013597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = -27.359013597 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = -27.359013597 + 11.125 x = -27.359013597 + 11.125 Combine like terms: -27.359013597 + 11.125 = -16.234013597 x = -16.234013597 Simplifying x = -16.234013597Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.484013597, -16.234013597}
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