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Simplifying 7x4 + -21x2 + -5 = 0 Reorder the terms: -5 + -21x2 + 7x4 = 0 Solving -5 + -21x2 + 7x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -3x2 + x4 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -3x2 + 0.7142857143 + x4 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -3x2 + x4 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -3x2 + x4 = 0 + 0.7142857143 -3x2 + x4 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -3x2 + x4 = 0.7142857143 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = 0.7142857143 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 0.7142857143 + 2.25 Combine like terms: 0.7142857143 + 2.25 = 2.9642857143 2.25 + -3x2 + x4 = 2.9642857143 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 2.9642857143 Calculate the square root of the right side: 1.721710113 Break this problem into two subproblems by setting (x2 + -1.5) equal to 1.721710113 and -1.721710113.Subproblem 1
x2 + -1.5 = 1.721710113 Simplifying x2 + -1.5 = 1.721710113 Reorder the terms: -1.5 + x2 = 1.721710113 Solving -1.5 + x2 = 1.721710113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 1.721710113 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 1.721710113 + 1.5 x2 = 1.721710113 + 1.5 Combine like terms: 1.721710113 + 1.5 = 3.221710113 x2 = 3.221710113 Simplifying x2 = 3.221710113 Take the square root of each side: x = {-1.794912286, 1.794912286}Subproblem 2
x2 + -1.5 = -1.721710113 Simplifying x2 + -1.5 = -1.721710113 Reorder the terms: -1.5 + x2 = -1.721710113 Solving -1.5 + x2 = -1.721710113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -1.721710113 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -1.721710113 + 1.5 x2 = -1.721710113 + 1.5 Combine like terms: -1.721710113 + 1.5 = -0.221710113 x2 = -0.221710113 Simplifying x2 = -0.221710113 Reorder the terms: 0.221710113 + x2 = -0.221710113 + 0.221710113 Combine like terms: -0.221710113 + 0.221710113 = 0.000000000 0.221710113 + 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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