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Simplifying 5y4 + -14y2 + 3 = 0 Reorder the terms: 3 + -14y2 + 5y4 = 0 Solving 3 + -14y2 + 5y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -2.8y2 + y4 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.8y2 + -0.6 + y4 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.8y2 + y4 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.8y2 + y4 = 0 + -0.6 -2.8y2 + y4 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.8y2 + y4 = -0.6 The y term is -2.8y2. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8y2 + 1.96 + y4 = -0.6 + 1.96 Reorder the terms: 1.96 + -2.8y2 + y4 = -0.6 + 1.96 Combine like terms: -0.6 + 1.96 = 1.36 1.96 + -2.8y2 + y4 = 1.36 Factor a perfect square on the left side: (y2 + -1.4)(y2 + -1.4) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (y2 + -1.4) equal to 1.166190379 and -1.166190379.Subproblem 1
y2 + -1.4 = 1.166190379 Simplifying y2 + -1.4 = 1.166190379 Reorder the terms: -1.4 + y2 = 1.166190379 Solving -1.4 + y2 = 1.166190379 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + y2 = 1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + y2 = 1.166190379 + 1.4 y2 = 1.166190379 + 1.4 Combine like terms: 1.166190379 + 1.4 = 2.566190379 y2 = 2.566190379 Simplifying y2 = 2.566190379 Take the square root of each side: y = {-1.601933325, 1.601933325}Subproblem 2
y2 + -1.4 = -1.166190379 Simplifying y2 + -1.4 = -1.166190379 Reorder the terms: -1.4 + y2 = -1.166190379 Solving -1.4 + y2 = -1.166190379 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + y2 = -1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + y2 = -1.166190379 + 1.4 y2 = -1.166190379 + 1.4 Combine like terms: -1.166190379 + 1.4 = 0.233809621 y2 = 0.233809621 Simplifying y2 = 0.233809621 Take the square root of each side: y = {-0.483538645, 0.483538645}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.601933325, 1.601933325, -0.483538645, 0.483538645}
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