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Simplifying 4x4 + -39x2 + -20 = 0 Reorder the terms: -20 + -39x2 + 4x4 = 0 Solving -20 + -39x2 + 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 + -9.75x2 + x4 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -9.75x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + -9.75x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9.75x2 + x4 = 0 + 5 -9.75x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 -9.75x2 + x4 = 5 The x term is -9.75x2. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x2 + 23.765625 + x4 = 5 + 23.765625 Reorder the terms: 23.765625 + -9.75x2 + x4 = 5 + 23.765625 Combine like terms: 5 + 23.765625 = 28.765625 23.765625 + -9.75x2 + x4 = 28.765625 Factor a perfect square on the left side: (x2 + -4.875)(x2 + -4.875) = 28.765625 Calculate the square root of the right side: 5.363359488 Break this problem into two subproblems by setting (x2 + -4.875) equal to 5.363359488 and -5.363359488.Subproblem 1
x2 + -4.875 = 5.363359488 Simplifying x2 + -4.875 = 5.363359488 Reorder the terms: -4.875 + x2 = 5.363359488 Solving -4.875 + x2 = 5.363359488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x2 = 5.363359488 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x2 = 5.363359488 + 4.875 x2 = 5.363359488 + 4.875 Combine like terms: 5.363359488 + 4.875 = 10.238359488 x2 = 10.238359488 Simplifying x2 = 10.238359488 Take the square root of each side: x = {-3.19974366, 3.19974366}Subproblem 2
x2 + -4.875 = -5.363359488 Simplifying x2 + -4.875 = -5.363359488 Reorder the terms: -4.875 + x2 = -5.363359488 Solving -4.875 + x2 = -5.363359488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x2 = -5.363359488 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x2 = -5.363359488 + 4.875 x2 = -5.363359488 + 4.875 Combine like terms: -5.363359488 + 4.875 = -0.488359488 x2 = -0.488359488 Simplifying x2 = -0.488359488 Reorder the terms: 0.488359488 + x2 = -0.488359488 + 0.488359488 Combine like terms: -0.488359488 + 0.488359488 = 0.000000000 0.488359488 + 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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