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Simplifying 20 + 3y = 4y2 Solving 20 + 3y = 4y2 Solving for variable 'y'. Combine like terms: 4y2 + -4y2 = 0 20 + 3y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5 + -0.75y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.75y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -0.75y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.75y + y2 = 0 + 5 -0.75y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.75y + y2 = 5 The y term is -0.75y. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75y + 0.140625 + y2 = 5 + 0.140625 Reorder the terms: 0.140625 + -0.75y + y2 = 5 + 0.140625 Combine like terms: 5 + 0.140625 = 5.140625 0.140625 + -0.75y + y2 = 5.140625 Factor a perfect square on the left side: (y + -0.375)(y + -0.375) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (y + -0.375) equal to 2.267294643 and -2.267294643.Subproblem 1
y + -0.375 = 2.267294643 Simplifying y + -0.375 = 2.267294643 Reorder the terms: -0.375 + y = 2.267294643 Solving -0.375 + y = 2.267294643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = 2.267294643 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = 2.267294643 + 0.375 y = 2.267294643 + 0.375 Combine like terms: 2.267294643 + 0.375 = 2.642294643 y = 2.642294643 Simplifying y = 2.642294643Subproblem 2
y + -0.375 = -2.267294643 Simplifying y + -0.375 = -2.267294643 Reorder the terms: -0.375 + y = -2.267294643 Solving -0.375 + y = -2.267294643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = -2.267294643 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = -2.267294643 + 0.375 y = -2.267294643 + 0.375 Combine like terms: -2.267294643 + 0.375 = -1.892294643 y = -1.892294643 Simplifying y = -1.892294643Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.642294643, -1.892294643}
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