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Simplifying -4y2 + -20y + 3 = 0 Reorder the terms: 3 + -20y + -4y2 = 0 Solving 3 + -20y + -4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + 5y + y2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 5y + 0.75 + y2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 5y + y2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 5y + y2 = 0 + 0.75 5y + y2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 5y + y2 = 0.75 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 = 0.75 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 0.75 + 6.25 Combine like terms: 0.75 + 6.25 = 7 6.25 + 5y + y2 = 7 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + 2.5) equal to 2.645751311 and -2.645751311.Subproblem 1
y + 2.5 = 2.645751311 Simplifying y + 2.5 = 2.645751311 Reorder the terms: 2.5 + y = 2.645751311 Solving 2.5 + y = 2.645751311 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 = 2.645751311 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 2.645751311 + -2.5 y = 2.645751311 + -2.5 Combine like terms: 2.645751311 + -2.5 = 0.145751311 y = 0.145751311 Simplifying y = 0.145751311Subproblem 2
y + 2.5 = -2.645751311 Simplifying y + 2.5 = -2.645751311 Reorder the terms: 2.5 + y = -2.645751311 Solving 2.5 + y = -2.645751311 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 = -2.645751311 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -2.645751311 + -2.5 y = -2.645751311 + -2.5 Combine like terms: -2.645751311 + -2.5 = -5.145751311 y = -5.145751311 Simplifying y = -5.145751311Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.145751311, -5.145751311}
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