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Simplifying 0.64x2 + -6x + -5000 = 0 Reorder the terms: -5000 + -6x + 0.64x2 = 0 Solving -5000 + -6x + 0.64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. -7812.5 + -9.375x + x2 = 0 Move the constant term to the right: Add '7812.5' to each side of the equation. -7812.5 + -9.375x + 7812.5 + x2 = 0 + 7812.5 Reorder the terms: -7812.5 + 7812.5 + -9.375x + x2 = 0 + 7812.5 Combine like terms: -7812.5 + 7812.5 = 0.0 0.0 + -9.375x + x2 = 0 + 7812.5 -9.375x + x2 = 0 + 7812.5 Combine like terms: 0 + 7812.5 = 7812.5 -9.375x + x2 = 7812.5 The x term is -9.375x. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375x + 21.97265625 + x2 = 7812.5 + 21.97265625 Reorder the terms: 21.97265625 + -9.375x + x2 = 7812.5 + 21.97265625 Combine like terms: 7812.5 + 21.97265625 = 7834.47265625 21.97265625 + -9.375x + x2 = 7834.47265625 Factor a perfect square on the left side: (x + -4.6875)(x + -4.6875) = 7834.47265625 Calculate the square root of the right side: 88.512556489 Break this problem into two subproblems by setting (x + -4.6875) equal to 88.512556489 and -88.512556489.Subproblem 1
x + -4.6875 = 88.512556489 Simplifying x + -4.6875 = 88.512556489 Reorder the terms: -4.6875 + x = 88.512556489 Solving -4.6875 + x = 88.512556489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = 88.512556489 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = 88.512556489 + 4.6875 x = 88.512556489 + 4.6875 Combine like terms: 88.512556489 + 4.6875 = 93.200056489 x = 93.200056489 Simplifying x = 93.200056489Subproblem 2
x + -4.6875 = -88.512556489 Simplifying x + -4.6875 = -88.512556489 Reorder the terms: -4.6875 + x = -88.512556489 Solving -4.6875 + x = -88.512556489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = -88.512556489 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = -88.512556489 + 4.6875 x = -88.512556489 + 4.6875 Combine like terms: -88.512556489 + 4.6875 = -83.825056489 x = -83.825056489 Simplifying x = -83.825056489Solution
The solution to the problem is based on the solutions from the subproblems. x = {93.200056489, -83.825056489}
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