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Simplifying 1000x2 + 64x + -57.6 = 0 Reorder the terms: -57.6 + 64x + 1000x2 = 0 Solving -57.6 + 64x + 1000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. -0.0576 + 0.064x + x2 = 0 Move the constant term to the right: Add '0.0576' to each side of the equation. -0.0576 + 0.064x + 0.0576 + x2 = 0 + 0.0576 Reorder the terms: -0.0576 + 0.0576 + 0.064x + x2 = 0 + 0.0576 Combine like terms: -0.0576 + 0.0576 = 0.0000 0.0000 + 0.064x + x2 = 0 + 0.0576 0.064x + x2 = 0 + 0.0576 Combine like terms: 0 + 0.0576 = 0.0576 0.064x + x2 = 0.0576 The x term is 0.064x. Take half its coefficient (0.032). Square it (0.001024) and add it to both sides. Add '0.001024' to each side of the equation. 0.064x + 0.001024 + x2 = 0.0576 + 0.001024 Reorder the terms: 0.001024 + 0.064x + x2 = 0.0576 + 0.001024 Combine like terms: 0.0576 + 0.001024 = 0.058624 0.001024 + 0.064x + x2 = 0.058624 Factor a perfect square on the left side: (x + 0.032)(x + 0.032) = 0.058624 Calculate the square root of the right side: 0.242123935 Break this problem into two subproblems by setting (x + 0.032) equal to 0.242123935 and -0.242123935.Subproblem 1
x + 0.032 = 0.242123935 Simplifying x + 0.032 = 0.242123935 Reorder the terms: 0.032 + x = 0.242123935 Solving 0.032 + x = 0.242123935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.032' to each side of the equation. 0.032 + -0.032 + x = 0.242123935 + -0.032 Combine like terms: 0.032 + -0.032 = 0.000 0.000 + x = 0.242123935 + -0.032 x = 0.242123935 + -0.032 Combine like terms: 0.242123935 + -0.032 = 0.210123935 x = 0.210123935 Simplifying x = 0.210123935Subproblem 2
x + 0.032 = -0.242123935 Simplifying x + 0.032 = -0.242123935 Reorder the terms: 0.032 + x = -0.242123935 Solving 0.032 + x = -0.242123935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.032' to each side of the equation. 0.032 + -0.032 + x = -0.242123935 + -0.032 Combine like terms: 0.032 + -0.032 = 0.000 0.000 + x = -0.242123935 + -0.032 x = -0.242123935 + -0.032 Combine like terms: -0.242123935 + -0.032 = -0.274123935 x = -0.274123935 Simplifying x = -0.274123935Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.210123935, -0.274123935}
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