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Simplifying -2x4 + 46x2 = -1000 Reorder the terms: 46x2 + -2x4 = -1000 Solving 46x2 + -2x4 = -1000 Solving for variable 'x'. Reorder the terms: 1000 + 46x2 + -2x4 = -1000 + 1000 Combine like terms: -1000 + 1000 = 0 1000 + 46x2 + -2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(500 + 23x2 + -1x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(500 + 23x2 + -1x4)' equal to zero and attempt to solve: Simplifying 500 + 23x2 + -1x4 = 0 Solving 500 + 23x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -500 + -23x2 + x4 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -23x2 + 500 + x4 = 0 + 500 Reorder the terms: -500 + 500 + -23x2 + x4 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -23x2 + x4 = 0 + 500 -23x2 + x4 = 0 + 500 Combine like terms: 0 + 500 = 500 -23x2 + x4 = 500 The x term is -23x2. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x2 + 132.25 + x4 = 500 + 132.25 Reorder the terms: 132.25 + -23x2 + x4 = 500 + 132.25 Combine like terms: 500 + 132.25 = 632.25 132.25 + -23x2 + x4 = 632.25 Factor a perfect square on the left side: (x2 + -11.5)(x2 + -11.5) = 632.25 Calculate the square root of the right side: 25.144581921 Break this problem into two subproblems by setting (x2 + -11.5) equal to 25.144581921 and -25.144581921.Subproblem 1
x2 + -11.5 = 25.144581921 Simplifying x2 + -11.5 = 25.144581921 Reorder the terms: -11.5 + x2 = 25.144581921 Solving -11.5 + x2 = 25.144581921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x2 = 25.144581921 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = 25.144581921 + 11.5 x2 = 25.144581921 + 11.5 Combine like terms: 25.144581921 + 11.5 = 36.644581921 x2 = 36.644581921 Simplifying x2 = 36.644581921 Take the square root of each side: x = {-6.053476846, 6.053476846}Subproblem 2
x2 + -11.5 = -25.144581921 Simplifying x2 + -11.5 = -25.144581921 Reorder the terms: -11.5 + x2 = -25.144581921 Solving -11.5 + x2 = -25.144581921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x2 = -25.144581921 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = -25.144581921 + 11.5 x2 = -25.144581921 + 11.5 Combine like terms: -25.144581921 + 11.5 = -13.644581921 x2 = -13.644581921 Simplifying x2 = -13.644581921 Reorder the terms: 13.644581921 + x2 = -13.644581921 + 13.644581921 Combine like terms: -13.644581921 + 13.644581921 = 0.000000000 13.644581921 + 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. 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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