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Simplifying 1000 = x2 + (x3 * 2x) Reorder the terms for easier multiplication: 1000 = x2 + (2x3 * x) Multiply x3 * x 1000 = x2 + (2x4) Solving 1000 = x2 + (2x4) Solving for variable 'x'. Reorder the terms: 1000 + -1x2 + (-2x4) = x2 + -1x2 + (2x4) + (-2x4) Combine like terms: x2 + -1x2 = 0 1000 + -1x2 + (-2x4) = 0 + (2x4) + (-2x4) 1000 + -1x2 + (-2x4) = (2x4) + (-2x4) Combine like terms: (2x4) + (-2x4) = 0 1000 + -1x2 + (-2x4) = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -500 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + 0.5x2 + 500 + x4 = 0 + 500 Reorder the terms: -500 + 500 + 0.5x2 + x4 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 0.5x2 + x4 = 0 + 500 0.5x2 + x4 = 0 + 500 Combine like terms: 0 + 500 = 500 0.5x2 + x4 = 500 The x term is 0.5x2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x2 + 0.0625 + x4 = 500 + 0.0625 Reorder the terms: 0.0625 + 0.5x2 + x4 = 500 + 0.0625 Combine like terms: 500 + 0.0625 = 500.0625 0.0625 + 0.5x2 + x4 = 500.0625 Factor a perfect square on the left side: ((x2) + 0.25)((x2) + 0.25) = 500.0625 Calculate the square root of the right side: 22.362077274 Break this problem into two subproblems by setting ((x2) + 0.25) equal to 22.362077274 and -22.362077274.Subproblem 1
(x2) + 0.25 = 22.362077274 Simplifying (x2) + 0.25 = 22.362077274 x2 + 0.25 = 22.362077274 Reorder the terms: 0.25 + x2 = 22.362077274 Solving 0.25 + x2 = 22.362077274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = 22.362077274 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 22.362077274 + -0.25 x2 = 22.362077274 + -0.25 Combine like terms: 22.362077274 + -0.25 = 22.112077274 x2 = 22.112077274 Simplifying x2 = 22.112077274 Take the square root of each side: x = {-4.70234806, 4.70234806}Subproblem 2
(x2) + 0.25 = -22.362077274 Simplifying (x2) + 0.25 = -22.362077274 x2 + 0.25 = -22.362077274 Reorder the terms: 0.25 + x2 = -22.362077274 Solving 0.25 + x2 = -22.362077274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = -22.362077274 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = -22.362077274 + -0.25 x2 = -22.362077274 + -0.25 Combine like terms: -22.362077274 + -0.25 = -22.612077274 x2 = -22.612077274 Simplifying x2 = -22.612077274 Reorder the terms: 22.612077274 + x2 = -22.612077274 + 22.612077274 Combine like terms: -22.612077274 + 22.612077274 = 0.000000000 22.612077274 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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