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Simplifying 4x4 + 20x2 + -23 = 0 Reorder the terms: -23 + 20x2 + 4x4 = 0 Solving -23 + 20x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + 5x2 + x4 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 5x2 + 5.75 + x4 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + 5x2 + x4 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 5x2 + x4 = 0 + 5.75 5x2 + x4 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 5x2 + x4 = 5.75 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = 5.75 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = 5.75 + 6.25 Combine like terms: 5.75 + 6.25 = 12 6.25 + 5x2 + x4 = 12 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x2 + 2.5) equal to 3.464101615 and -3.464101615.Subproblem 1
x2 + 2.5 = 3.464101615 Simplifying x2 + 2.5 = 3.464101615 Reorder the terms: 2.5 + x2 = 3.464101615 Solving 2.5 + x2 = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 3.464101615 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 3.464101615 + -2.5 x2 = 3.464101615 + -2.5 Combine like terms: 3.464101615 + -2.5 = 0.964101615 x2 = 0.964101615 Simplifying x2 = 0.964101615 Take the square root of each side: x = {-0.981886763, 0.981886763}Subproblem 2
x2 + 2.5 = -3.464101615 Simplifying x2 + 2.5 = -3.464101615 Reorder the terms: 2.5 + x2 = -3.464101615 Solving 2.5 + x2 = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -3.464101615 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -3.464101615 + -2.5 x2 = -3.464101615 + -2.5 Combine like terms: -3.464101615 + -2.5 = -5.964101615 x2 = -5.964101615 Simplifying x2 = -5.964101615 Reorder the terms: 5.964101615 + x2 = -5.964101615 + 5.964101615 Combine like terms: -5.964101615 + 5.964101615 = 0.000000000 5.964101615 + 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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