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Simplifying 0 = x4 + -3x2 + -3 Reorder the terms: 0 = -3 + -3x2 + x4 Solving 0 = -3 + -3x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + 3x2 + -1x4 = -3 + -3x2 + x4 + 3 + 3x2 + -1x4 Reorder the terms: 3 + 3x2 + -1x4 = -3 + 3 + -3x2 + 3x2 + x4 + -1x4 Combine like terms: -3 + 3 = 0 3 + 3x2 + -1x4 = 0 + -3x2 + 3x2 + x4 + -1x4 3 + 3x2 + -1x4 = -3x2 + 3x2 + x4 + -1x4 Combine like terms: -3x2 + 3x2 = 0 3 + 3x2 + -1x4 = 0 + x4 + -1x4 3 + 3x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 3 + 3x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -3x2 + x4 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3x2 + 3 + x4 = 0 + 3 Reorder the terms: -3 + 3 + -3x2 + x4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3x2 + x4 = 0 + 3 -3x2 + x4 = 0 + 3 Combine like terms: 0 + 3 = 3 -3x2 + x4 = 3 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = 3 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3x2 + x4 = 5.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x2 + -1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x2 + -1.5 = 2.291287847 Simplifying x2 + -1.5 = 2.291287847 Reorder the terms: -1.5 + x2 = 2.291287847 Solving -1.5 + x2 = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 2.291287847 + 1.5 x2 = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 x2 = 3.791287847 Simplifying x2 = 3.791287847 Take the square root of each side: x = {-1.947122967, 1.947122967}Subproblem 2
x2 + -1.5 = -2.291287847 Simplifying x2 + -1.5 = -2.291287847 Reorder the terms: -1.5 + x2 = -2.291287847 Solving -1.5 + x2 = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -2.291287847 + 1.5 x2 = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 x2 = -0.791287847 Simplifying x2 = -0.791287847 Reorder the terms: 0.791287847 + x2 = -0.791287847 + 0.791287847 Combine like terms: -0.791287847 + 0.791287847 = 0.000000000 0.791287847 + 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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