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Simplifying 6x4 + -17x2 + -5 = 0 Reorder the terms: -5 + -17x2 + 6x4 = 0 Solving -5 + -17x2 + 6x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -2.833333333x2 + x4 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -2.833333333x2 + 0.8333333333 + x4 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -2.833333333x2 + x4 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -2.833333333x2 + x4 = 0 + 0.8333333333 -2.833333333x2 + x4 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -2.833333333x2 + x4 = 0.8333333333 The x term is -2.833333333x2. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x2 + 2.006944445 + x4 = 0.8333333333 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x2 + x4 = 0.8333333333 + 2.006944445 Combine like terms: 0.8333333333 + 2.006944445 = 2.8402777783 2.006944445 + -2.833333333x2 + x4 = 2.8402777783 Factor a perfect square on the left side: (x2 + -1.416666667)(x2 + -1.416666667) = 2.8402777783 Calculate the square root of the right side: 1.685312368 Break this problem into two subproblems by setting (x2 + -1.416666667) equal to 1.685312368 and -1.685312368.Subproblem 1
x2 + -1.416666667 = 1.685312368 Simplifying x2 + -1.416666667 = 1.685312368 Reorder the terms: -1.416666667 + x2 = 1.685312368 Solving -1.416666667 + x2 = 1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x2 = 1.685312368 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x2 = 1.685312368 + 1.416666667 x2 = 1.685312368 + 1.416666667 Combine like terms: 1.685312368 + 1.416666667 = 3.101979035 x2 = 3.101979035 Simplifying x2 = 3.101979035 Take the square root of each side: x = {-1.761243605, 1.761243605}Subproblem 2
x2 + -1.416666667 = -1.685312368 Simplifying x2 + -1.416666667 = -1.685312368 Reorder the terms: -1.416666667 + x2 = -1.685312368 Solving -1.416666667 + x2 = -1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x2 = -1.685312368 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x2 = -1.685312368 + 1.416666667 x2 = -1.685312368 + 1.416666667 Combine like terms: -1.685312368 + 1.416666667 = -0.268645701 x2 = -0.268645701 Simplifying x2 = -0.268645701 Reorder the terms: 0.268645701 + x2 = -0.268645701 + 0.268645701 Combine like terms: -0.268645701 + 0.268645701 = 0.000000000 0.268645701 + 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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