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Simplifying 4y2 + 19 = 20y Reorder the terms: 19 + 4y2 = 20y Solving 19 + 4y2 = 20y Solving for variable 'y'. Reorder the terms: 19 + -20y + 4y2 = 20y + -20y Combine like terms: 20y + -20y = 0 19 + -20y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.75 + -5y + y2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + -5y + -4.75 + y2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + -5y + y2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + -5y + y2 = 0 + -4.75 -5y + y2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 -5y + y2 = -4.75 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = -4.75 + 6.25 Reorder the terms: 6.25 + -5y + y2 = -4.75 + 6.25 Combine like terms: -4.75 + 6.25 = 1.5 6.25 + -5y + y2 = 1.5 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (y + -2.5) equal to 1.224744871 and -1.224744871.Subproblem 1
y + -2.5 = 1.224744871 Simplifying y + -2.5 = 1.224744871 Reorder the terms: -2.5 + y = 1.224744871 Solving -2.5 + y = 1.224744871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 1.224744871 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 1.224744871 + 2.5 y = 1.224744871 + 2.5 Combine like terms: 1.224744871 + 2.5 = 3.724744871 y = 3.724744871 Simplifying y = 3.724744871Subproblem 2
y + -2.5 = -1.224744871 Simplifying y + -2.5 = -1.224744871 Reorder the terms: -2.5 + y = -1.224744871 Solving -2.5 + y = -1.224744871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -1.224744871 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -1.224744871 + 2.5 y = -1.224744871 + 2.5 Combine like terms: -1.224744871 + 2.5 = 1.275255129 y = 1.275255129 Simplifying y = 1.275255129Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.724744871, 1.275255129}
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