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Simplifying x = 16x2 + 368x + -2035 Reorder the terms: x = -2035 + 368x + 16x2 Solving x = -2035 + 368x + 16x2 Solving for variable 'x'. Reorder the terms: 2035 + x + -368x + -16x2 = -2035 + 368x + 16x2 + 2035 + -368x + -16x2 Combine like terms: x + -368x = -367x 2035 + -367x + -16x2 = -2035 + 368x + 16x2 + 2035 + -368x + -16x2 Reorder the terms: 2035 + -367x + -16x2 = -2035 + 2035 + 368x + -368x + 16x2 + -16x2 Combine like terms: -2035 + 2035 = 0 2035 + -367x + -16x2 = 0 + 368x + -368x + 16x2 + -16x2 2035 + -367x + -16x2 = 368x + -368x + 16x2 + -16x2 Combine like terms: 368x + -368x = 0 2035 + -367x + -16x2 = 0 + 16x2 + -16x2 2035 + -367x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 2035 + -367x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -127.1875 + 22.9375x + x2 = 0 Move the constant term to the right: Add '127.1875' to each side of the equation. -127.1875 + 22.9375x + 127.1875 + x2 = 0 + 127.1875 Reorder the terms: -127.1875 + 127.1875 + 22.9375x + x2 = 0 + 127.1875 Combine like terms: -127.1875 + 127.1875 = 0.0000 0.0000 + 22.9375x + x2 = 0 + 127.1875 22.9375x + x2 = 0 + 127.1875 Combine like terms: 0 + 127.1875 = 127.1875 22.9375x + x2 = 127.1875 The x term is 22.9375x. Take half its coefficient (11.46875). Square it (131.5322266) and add it to both sides. Add '131.5322266' to each side of the equation. 22.9375x + 131.5322266 + x2 = 127.1875 + 131.5322266 Reorder the terms: 131.5322266 + 22.9375x + x2 = 127.1875 + 131.5322266 Combine like terms: 127.1875 + 131.5322266 = 258.7197266 131.5322266 + 22.9375x + x2 = 258.7197266 Factor a perfect square on the left side: (x + 11.46875)(x + 11.46875) = 258.7197266 Calculate the square root of the right side: 16.084766912 Break this problem into two subproblems by setting (x + 11.46875) equal to 16.084766912 and -16.084766912.Subproblem 1
x + 11.46875 = 16.084766912 Simplifying x + 11.46875 = 16.084766912 Reorder the terms: 11.46875 + x = 16.084766912 Solving 11.46875 + x = 16.084766912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.46875' to each side of the equation. 11.46875 + -11.46875 + x = 16.084766912 + -11.46875 Combine like terms: 11.46875 + -11.46875 = 0.00000 0.00000 + x = 16.084766912 + -11.46875 x = 16.084766912 + -11.46875 Combine like terms: 16.084766912 + -11.46875 = 4.616016912 x = 4.616016912 Simplifying x = 4.616016912Subproblem 2
x + 11.46875 = -16.084766912 Simplifying x + 11.46875 = -16.084766912 Reorder the terms: 11.46875 + x = -16.084766912 Solving 11.46875 + x = -16.084766912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.46875' to each side of the equation. 11.46875 + -11.46875 + x = -16.084766912 + -11.46875 Combine like terms: 11.46875 + -11.46875 = 0.00000 0.00000 + x = -16.084766912 + -11.46875 x = -16.084766912 + -11.46875 Combine like terms: -16.084766912 + -11.46875 = -27.553516912 x = -27.553516912 Simplifying x = -27.553516912Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.616016912, -27.553516912}
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