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Simplifying 2x4 + x2 + -9 = 0 Reorder the terms: -9 + x2 + 2x4 = 0 Solving -9 + x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.5x2 + 4.5 + x4 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.5x2 + x4 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.5x2 + x4 = 0 + 4.5 0.5x2 + x4 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 0.5x2 + x4 = 4.5 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x2 + 0.25 + x4 = 4.5 + 0.25 Reorder the terms: 0.25 + 0.5x2 + x4 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + 0.5x2 + x4 = 4.75 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x2 + 0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x2 + 0.5 = 2.179449472 Simplifying x2 + 0.5 = 2.179449472 Reorder the terms: 0.5 + x2 = 2.179449472 Solving 0.5 + x2 = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 2.179449472 + -0.5 x2 = 2.179449472 + -0.5 Combine like terms: 2.179449472 + -0.5 = 1.679449472 x2 = 1.679449472 Simplifying x2 = 1.679449472 Take the square root of each side: x = {-1.295935751, 1.295935751}Subproblem 2
x2 + 0.5 = -2.179449472 Simplifying x2 + 0.5 = -2.179449472 Reorder the terms: 0.5 + x2 = -2.179449472 Solving 0.5 + x2 = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -2.179449472 + -0.5 x2 = -2.179449472 + -0.5 Combine like terms: -2.179449472 + -0.5 = -2.679449472 x2 = -2.679449472 Simplifying x2 = -2.679449472 Reorder the terms: 2.679449472 + x2 = -2.679449472 + 2.679449472 Combine like terms: -2.679449472 + 2.679449472 = 0.000000000 2.679449472 + 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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