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Simplifying y2(y2 + -4) = 3y2 + -4 Reorder the terms: y2(-4 + y2) = 3y2 + -4 (-4 * y2 + y2 * y2) = 3y2 + -4 (-4y2 + y4) = 3y2 + -4 Reorder the terms: -4y2 + y4 = -4 + 3y2 Solving -4y2 + y4 = -4 + 3y2 Solving for variable 'y'. Reorder the terms: 4 + -4y2 + -3y2 + y4 = -4 + 3y2 + 4 + -3y2 Combine like terms: -4y2 + -3y2 = -7y2 4 + -7y2 + y4 = -4 + 3y2 + 4 + -3y2 Reorder the terms: 4 + -7y2 + y4 = -4 + 4 + 3y2 + -3y2 Combine like terms: -4 + 4 = 0 4 + -7y2 + y4 = 0 + 3y2 + -3y2 4 + -7y2 + y4 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 4 + -7y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7y2 + -4 + y4 = 0 + -4 Reorder the terms: 4 + -4 + -7y2 + y4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7y2 + y4 = 0 + -4 -7y2 + y4 = 0 + -4 Combine like terms: 0 + -4 = -4 -7y2 + y4 = -4 The y term is -7y2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y2 + 12.25 + y4 = -4 + 12.25 Reorder the terms: 12.25 + -7y2 + y4 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + -7y2 + y4 = 8.25 Factor a perfect square on the left side: (y2 + -3.5)(y2 + -3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (y2 + -3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
y2 + -3.5 = 2.872281323 Simplifying y2 + -3.5 = 2.872281323 Reorder the terms: -3.5 + y2 = 2.872281323 Solving -3.5 + y2 = 2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y2 = 2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y2 = 2.872281323 + 3.5 y2 = 2.872281323 + 3.5 Combine like terms: 2.872281323 + 3.5 = 6.372281323 y2 = 6.372281323 Simplifying y2 = 6.372281323 Take the square root of each side: y = {-2.524337799, 2.524337799}Subproblem 2
y2 + -3.5 = -2.872281323 Simplifying y2 + -3.5 = -2.872281323 Reorder the terms: -3.5 + y2 = -2.872281323 Solving -3.5 + y2 = -2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y2 = -2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y2 = -2.872281323 + 3.5 y2 = -2.872281323 + 3.5 Combine like terms: -2.872281323 + 3.5 = 0.627718677 y2 = 0.627718677 Simplifying y2 = 0.627718677 Take the square root of each side: y = {-0.792286992, 0.792286992}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.524337799, 2.524337799, -0.792286992, 0.792286992}
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