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Simplifying 5y4 + -7y2 + 1.5 = 0 Reorder the terms: 1.5 + -7y2 + 5y4 = 0 Solving 1.5 + -7y2 + 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'. 0.3 + -1.4y2 + y4 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -1.4y2 + -0.3 + y4 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + -1.4y2 + y4 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -1.4y2 + y4 = 0 + -0.3 -1.4y2 + y4 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 -1.4y2 + y4 = -0.3 The y term is -1.4y2. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4y2 + 0.49 + y4 = -0.3 + 0.49 Reorder the terms: 0.49 + -1.4y2 + y4 = -0.3 + 0.49 Combine like terms: -0.3 + 0.49 = 0.19 0.49 + -1.4y2 + y4 = 0.19 Factor a perfect square on the left side: (y2 + -0.7)(y2 + -0.7) = 0.19 Calculate the square root of the right side: 0.435889894 Break this problem into two subproblems by setting (y2 + -0.7) equal to 0.435889894 and -0.435889894.Subproblem 1
y2 + -0.7 = 0.435889894 Simplifying y2 + -0.7 = 0.435889894 Reorder the terms: -0.7 + y2 = 0.435889894 Solving -0.7 + y2 = 0.435889894 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y2 = 0.435889894 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y2 = 0.435889894 + 0.7 y2 = 0.435889894 + 0.7 Combine like terms: 0.435889894 + 0.7 = 1.135889894 y2 = 1.135889894 Simplifying y2 = 1.135889894 Take the square root of each side: y = {-1.065781354, 1.065781354}Subproblem 2
y2 + -0.7 = -0.435889894 Simplifying y2 + -0.7 = -0.435889894 Reorder the terms: -0.7 + y2 = -0.435889894 Solving -0.7 + y2 = -0.435889894 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y2 = -0.435889894 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y2 = -0.435889894 + 0.7 y2 = -0.435889894 + 0.7 Combine like terms: -0.435889894 + 0.7 = 0.264110106 y2 = 0.264110106 Simplifying y2 = 0.264110106 Take the square root of each side: y = {-0.513916439, 0.513916439}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.065781354, 1.065781354, -0.513916439, 0.513916439}
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