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Simplifying 4x4 + -7x2 + -4 = 0 Reorder the terms: -4 + -7x2 + 4x4 = 0 Solving -4 + -7x2 + 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'. -1 + -1.75x2 + x4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.75x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -1.75x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.75x2 + x4 = 0 + 1 -1.75x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.75x2 + x4 = 1 The x term is -1.75x2. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x2 + 0.765625 + x4 = 1 + 0.765625 Reorder the terms: 0.765625 + -1.75x2 + x4 = 1 + 0.765625 Combine like terms: 1 + 0.765625 = 1.765625 0.765625 + -1.75x2 + x4 = 1.765625 Factor a perfect square on the left side: (x2 + -0.875)(x2 + -0.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x2 + -0.875) equal to 1.328768227 and -1.328768227.Subproblem 1
x2 + -0.875 = 1.328768227 Simplifying x2 + -0.875 = 1.328768227 Reorder the terms: -0.875 + x2 = 1.328768227 Solving -0.875 + x2 = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x2 = 1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x2 = 1.328768227 + 0.875 x2 = 1.328768227 + 0.875 Combine like terms: 1.328768227 + 0.875 = 2.203768227 x2 = 2.203768227 Simplifying x2 = 2.203768227 Take the square root of each side: x = {-1.484509423, 1.484509423}Subproblem 2
x2 + -0.875 = -1.328768227 Simplifying x2 + -0.875 = -1.328768227 Reorder the terms: -0.875 + x2 = -1.328768227 Solving -0.875 + x2 = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x2 = -1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x2 = -1.328768227 + 0.875 x2 = -1.328768227 + 0.875 Combine like terms: -1.328768227 + 0.875 = -0.453768227 x2 = -0.453768227 Simplifying x2 = -0.453768227 Reorder the terms: 0.453768227 + x2 = -0.453768227 + 0.453768227 Combine like terms: -0.453768227 + 0.453768227 = 0.000000000 0.453768227 + 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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