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Simplifying 4x4 + 16x2 + -225 = 0 Reorder the terms: -225 + 16x2 + 4x4 = 0 Solving -225 + 16x2 + 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'. -56.25 + 4x2 + x4 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + 4x2 + 56.25 + x4 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + 4x2 + x4 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + 4x2 + x4 = 0 + 56.25 4x2 + x4 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 4x2 + x4 = 56.25 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 56.25 + 4 Reorder the terms: 4 + 4x2 + x4 = 56.25 + 4 Combine like terms: 56.25 + 4 = 60.25 4 + 4x2 + x4 = 60.25 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x2 + 2) equal to 7.762087348 and -7.762087348.Subproblem 1
x2 + 2 = 7.762087348 Simplifying x2 + 2 = 7.762087348 Reorder the terms: 2 + x2 = 7.762087348 Solving 2 + x2 = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 7.762087348 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 7.762087348 + -2 x2 = 7.762087348 + -2 Combine like terms: 7.762087348 + -2 = 5.762087348 x2 = 5.762087348 Simplifying x2 = 5.762087348 Take the square root of each side: x = {-2.400434825, 2.400434825}Subproblem 2
x2 + 2 = -7.762087348 Simplifying x2 + 2 = -7.762087348 Reorder the terms: 2 + x2 = -7.762087348 Solving 2 + x2 = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -7.762087348 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -7.762087348 + -2 x2 = -7.762087348 + -2 Combine like terms: -7.762087348 + -2 = -9.762087348 x2 = -9.762087348 Simplifying x2 = -9.762087348 Reorder the terms: 9.762087348 + x2 = -9.762087348 + 9.762087348 Combine like terms: -9.762087348 + 9.762087348 = 0.000000000 9.762087348 + 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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