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Simplifying 7x4 + -3x2 + -2 = 0 Reorder the terms: -2 + -3x2 + 7x4 = 0 Solving -2 + -3x2 + 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'. -0.2857142857 + -0.4285714286x2 + x4 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.4285714286x2 + 0.2857142857 + x4 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.4285714286x2 + x4 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.4285714286x2 + x4 = 0 + 0.2857142857 -0.4285714286x2 + x4 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.4285714286x2 + x4 = 0.2857142857 The x term is -0.4285714286x2. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x2 + 0.04591836735 + x4 = 0.2857142857 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x2 + x4 = 0.2857142857 + 0.04591836735 Combine like terms: 0.2857142857 + 0.04591836735 = 0.33163265305 0.04591836735 + -0.4285714286x2 + x4 = 0.33163265305 Factor a perfect square on the left side: (x2 + -0.2142857143)(x2 + -0.2142857143) = 0.33163265305 Calculate the square root of the right side: 0.575875553 Break this problem into two subproblems by setting (x2 + -0.2142857143) equal to 0.575875553 and -0.575875553.Subproblem 1
x2 + -0.2142857143 = 0.575875553 Simplifying x2 + -0.2142857143 = 0.575875553 Reorder the terms: -0.2142857143 + x2 = 0.575875553 Solving -0.2142857143 + x2 = 0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x2 = 0.575875553 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x2 = 0.575875553 + 0.2142857143 x2 = 0.575875553 + 0.2142857143 Combine like terms: 0.575875553 + 0.2142857143 = 0.7901612673 x2 = 0.7901612673 Simplifying x2 = 0.7901612673 Take the square root of each side: x = {-0.888910157, 0.888910157}Subproblem 2
x2 + -0.2142857143 = -0.575875553 Simplifying x2 + -0.2142857143 = -0.575875553 Reorder the terms: -0.2142857143 + x2 = -0.575875553 Solving -0.2142857143 + x2 = -0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x2 = -0.575875553 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x2 = -0.575875553 + 0.2142857143 x2 = -0.575875553 + 0.2142857143 Combine like terms: -0.575875553 + 0.2142857143 = -0.3615898387 x2 = -0.3615898387 Simplifying x2 = -0.3615898387 Reorder the terms: 0.3615898387 + x2 = -0.3615898387 + 0.3615898387 Combine like terms: -0.3615898387 + 0.3615898387 = 0.0000000000 0.3615898387 + 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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