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Simplifying 0.16x2 + -9x + -4000 = 0 Reorder the terms: -4000 + -9x + 0.16x2 = 0 Solving -4000 + -9x + 0.16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. -25000 + -56.25x + x2 = 0 Move the constant term to the right: Add '25000' to each side of the equation. -25000 + -56.25x + 25000 + x2 = 0 + 25000 Reorder the terms: -25000 + 25000 + -56.25x + x2 = 0 + 25000 Combine like terms: -25000 + 25000 = 0 0 + -56.25x + x2 = 0 + 25000 -56.25x + x2 = 0 + 25000 Combine like terms: 0 + 25000 = 25000 -56.25x + x2 = 25000 The x term is -56.25x. Take half its coefficient (-28.125). Square it (791.015625) and add it to both sides. Add '791.015625' to each side of the equation. -56.25x + 791.015625 + x2 = 25000 + 791.015625 Reorder the terms: 791.015625 + -56.25x + x2 = 25000 + 791.015625 Combine like terms: 25000 + 791.015625 = 25791.015625 791.015625 + -56.25x + x2 = 25791.015625 Factor a perfect square on the left side: (x + -28.125)(x + -28.125) = 25791.015625 Calculate the square root of the right side: 160.595814469 Break this problem into two subproblems by setting (x + -28.125) equal to 160.595814469 and -160.595814469.Subproblem 1
x + -28.125 = 160.595814469 Simplifying x + -28.125 = 160.595814469 Reorder the terms: -28.125 + x = 160.595814469 Solving -28.125 + x = 160.595814469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.125' to each side of the equation. -28.125 + 28.125 + x = 160.595814469 + 28.125 Combine like terms: -28.125 + 28.125 = 0.000 0.000 + x = 160.595814469 + 28.125 x = 160.595814469 + 28.125 Combine like terms: 160.595814469 + 28.125 = 188.720814469 x = 188.720814469 Simplifying x = 188.720814469Subproblem 2
x + -28.125 = -160.595814469 Simplifying x + -28.125 = -160.595814469 Reorder the terms: -28.125 + x = -160.595814469 Solving -28.125 + x = -160.595814469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.125' to each side of the equation. -28.125 + 28.125 + x = -160.595814469 + 28.125 Combine like terms: -28.125 + 28.125 = 0.000 0.000 + x = -160.595814469 + 28.125 x = -160.595814469 + 28.125 Combine like terms: -160.595814469 + 28.125 = -132.470814469 x = -132.470814469 Simplifying x = -132.470814469Solution
The solution to the problem is based on the solutions from the subproblems. x = {188.720814469, -132.470814469}
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