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Simplifying 7x4 + -4x2 + -4 = 0 Reorder the terms: -4 + -4x2 + 7x4 = 0 Solving -4 + -4x2 + 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'. -0.5714285714 + -0.5714285714x2 + x4 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.5714285714x2 + 0.5714285714 + x4 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.5714285714x2 + x4 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.5714285714x2 + x4 = 0 + 0.5714285714 -0.5714285714x2 + x4 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.5714285714x2 + x4 = 0.5714285714 The x term is -0.5714285714x2. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x2 + 0.08163265305 + x4 = 0.5714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x2 + x4 = 0.5714285714 + 0.08163265305 Combine like terms: 0.5714285714 + 0.08163265305 = 0.65306122445 0.08163265305 + -0.5714285714x2 + x4 = 0.65306122445 Factor a perfect square on the left side: (x2 + -0.2857142857)(x2 + -0.2857142857) = 0.65306122445 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (x2 + -0.2857142857) equal to 0.808122036 and -0.808122036.Subproblem 1
x2 + -0.2857142857 = 0.808122036 Simplifying x2 + -0.2857142857 = 0.808122036 Reorder the terms: -0.2857142857 + x2 = 0.808122036 Solving -0.2857142857 + x2 = 0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x2 = 0.808122036 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x2 = 0.808122036 + 0.2857142857 x2 = 0.808122036 + 0.2857142857 Combine like terms: 0.808122036 + 0.2857142857 = 1.0938363217 x2 = 1.0938363217 Simplifying x2 = 1.0938363217 Take the square root of each side: x = {-1.045866302, 1.045866302}Subproblem 2
x2 + -0.2857142857 = -0.808122036 Simplifying x2 + -0.2857142857 = -0.808122036 Reorder the terms: -0.2857142857 + x2 = -0.808122036 Solving -0.2857142857 + x2 = -0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x2 = -0.808122036 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x2 = -0.808122036 + 0.2857142857 x2 = -0.808122036 + 0.2857142857 Combine like terms: -0.808122036 + 0.2857142857 = -0.5224077503 x2 = -0.5224077503 Simplifying x2 = -0.5224077503 Reorder the terms: 0.5224077503 + x2 = -0.5224077503 + 0.5224077503 Combine like terms: -0.5224077503 + 0.5224077503 = 0.0000000000 0.5224077503 + x2 = 0.0000000000 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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