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Simplifying 4x4 + -4x2 + -9 = 0 Reorder the terms: -9 + -4x2 + 4x4 = 0 Solving -9 + -4x2 + 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'. -2.25 + -1x2 + x4 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1x2 + 2.25 + x4 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1x2 + x4 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1x2 + x4 = 0 + 2.25 -1x2 + x4 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1x2 + x4 = 2.25 The x term is -1x2. 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. -1x2 + 0.25 + x4 = 2.25 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 0.25 + -1x2 + x4 = 2.5 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x2 + -0.5) equal to 1.58113883 and -1.58113883.Subproblem 1
x2 + -0.5 = 1.58113883 Simplifying x2 + -0.5 = 1.58113883 Reorder the terms: -0.5 + x2 = 1.58113883 Solving -0.5 + x2 = 1.58113883 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 = 1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 1.58113883 + 0.5 x2 = 1.58113883 + 0.5 Combine like terms: 1.58113883 + 0.5 = 2.08113883 x2 = 2.08113883 Simplifying x2 = 2.08113883 Take the square root of each side: x = {-1.442615274, 1.442615274}Subproblem 2
x2 + -0.5 = -1.58113883 Simplifying x2 + -0.5 = -1.58113883 Reorder the terms: -0.5 + x2 = -1.58113883 Solving -0.5 + x2 = -1.58113883 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 = -1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -1.58113883 + 0.5 x2 = -1.58113883 + 0.5 Combine like terms: -1.58113883 + 0.5 = -1.08113883 x2 = -1.08113883 Simplifying x2 = -1.08113883 Reorder the terms: 1.08113883 + x2 = -1.08113883 + 1.08113883 Combine like terms: -1.08113883 + 1.08113883 = 0.00000000 1.08113883 + x2 = 0.00000000 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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