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Simplifying 500x2 + -15.68x + -15.68 = 0 Reorder the terms: -15.68 + -15.68x + 500x2 = 0 Solving -15.68 + -15.68x + 500x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 500 the coefficient of the squared term: Divide each side by '500'. -0.03136 + -0.03136x + x2 = 0 Move the constant term to the right: Add '0.03136' to each side of the equation. -0.03136 + -0.03136x + 0.03136 + x2 = 0 + 0.03136 Reorder the terms: -0.03136 + 0.03136 + -0.03136x + x2 = 0 + 0.03136 Combine like terms: -0.03136 + 0.03136 = 0.00000 0.00000 + -0.03136x + x2 = 0 + 0.03136 -0.03136x + x2 = 0 + 0.03136 Combine like terms: 0 + 0.03136 = 0.03136 -0.03136x + x2 = 0.03136 The x term is -0.03136x. Take half its coefficient (-0.01568). Square it (0.0002458624) and add it to both sides. Add '0.0002458624' to each side of the equation. -0.03136x + 0.0002458624 + x2 = 0.03136 + 0.0002458624 Reorder the terms: 0.0002458624 + -0.03136x + x2 = 0.03136 + 0.0002458624 Combine like terms: 0.03136 + 0.0002458624 = 0.0316058624 0.0002458624 + -0.03136x + x2 = 0.0316058624 Factor a perfect square on the left side: (x + -0.01568)(x + -0.01568) = 0.0316058624 Calculate the square root of the right side: 0.177780377 Break this problem into two subproblems by setting (x + -0.01568) equal to 0.177780377 and -0.177780377.Subproblem 1
x + -0.01568 = 0.177780377 Simplifying x + -0.01568 = 0.177780377 Reorder the terms: -0.01568 + x = 0.177780377 Solving -0.01568 + x = 0.177780377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01568' to each side of the equation. -0.01568 + 0.01568 + x = 0.177780377 + 0.01568 Combine like terms: -0.01568 + 0.01568 = 0.00000 0.00000 + x = 0.177780377 + 0.01568 x = 0.177780377 + 0.01568 Combine like terms: 0.177780377 + 0.01568 = 0.193460377 x = 0.193460377 Simplifying x = 0.193460377Subproblem 2
x + -0.01568 = -0.177780377 Simplifying x + -0.01568 = -0.177780377 Reorder the terms: -0.01568 + x = -0.177780377 Solving -0.01568 + x = -0.177780377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01568' to each side of the equation. -0.01568 + 0.01568 + x = -0.177780377 + 0.01568 Combine like terms: -0.01568 + 0.01568 = 0.00000 0.00000 + x = -0.177780377 + 0.01568 x = -0.177780377 + 0.01568 Combine like terms: -0.177780377 + 0.01568 = -0.162100377 x = -0.162100377 Simplifying x = -0.162100377Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.193460377, -0.162100377}
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