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Simplifying 6y4 + -10y2 + 3 = 0 Reorder the terms: 3 + -10y2 + 6y4 = 0 Solving 3 + -10y2 + 6y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + -1.666666667y2 + y4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.666666667y2 + -0.5 + y4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.666666667y2 + y4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.666666667y2 + y4 = 0 + -0.5 -1.666666667y2 + y4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.666666667y2 + y4 = -0.5 The y term is -1.666666667y2. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667y2 + 0.6944444447 + y4 = -0.5 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667y2 + y4 = -0.5 + 0.6944444447 Combine like terms: -0.5 + 0.6944444447 = 0.1944444447 0.6944444447 + -1.666666667y2 + y4 = 0.1944444447 Factor a perfect square on the left side: (y2 + -0.8333333335)(y2 + -0.8333333335) = 0.1944444447 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (y2 + -0.8333333335) equal to 0.440958552 and -0.440958552.Subproblem 1
y2 + -0.8333333335 = 0.440958552 Simplifying y2 + -0.8333333335 = 0.440958552 Reorder the terms: -0.8333333335 + y2 = 0.440958552 Solving -0.8333333335 + y2 = 0.440958552 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + y2 = 0.440958552 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + y2 = 0.440958552 + 0.8333333335 y2 = 0.440958552 + 0.8333333335 Combine like terms: 0.440958552 + 0.8333333335 = 1.2742918855 y2 = 1.2742918855 Simplifying y2 = 1.2742918855 Take the square root of each side: y = {-1.128845377, 1.128845377}Subproblem 2
y2 + -0.8333333335 = -0.440958552 Simplifying y2 + -0.8333333335 = -0.440958552 Reorder the terms: -0.8333333335 + y2 = -0.440958552 Solving -0.8333333335 + y2 = -0.440958552 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + y2 = -0.440958552 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + y2 = -0.440958552 + 0.8333333335 y2 = -0.440958552 + 0.8333333335 Combine like terms: -0.440958552 + 0.8333333335 = 0.3923747815 y2 = 0.3923747815 Simplifying y2 = 0.3923747815 Take the square root of each side: y = {-0.626398261, 0.626398261}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.128845377, 1.128845377, -0.626398261, 0.626398261}
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