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Simplifying -4y2 + -20y + 7 = 0 Reorder the terms: 7 + -20y + -4y2 = 0 Solving 7 + -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'. -1.75 + 5y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 5y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 5y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 5y + y2 = 0 + 1.75 5y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 5y + y2 = 1.75 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 = 1.75 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 1.75 + 6.25 Combine like terms: 1.75 + 6.25 = 8 6.25 + 5y + y2 = 8 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y + 2.5) equal to 2.828427125 and -2.828427125.Subproblem 1
y + 2.5 = 2.828427125 Simplifying y + 2.5 = 2.828427125 Reorder the terms: 2.5 + y = 2.828427125 Solving 2.5 + y = 2.828427125 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 = 2.828427125 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 2.828427125 + -2.5 y = 2.828427125 + -2.5 Combine like terms: 2.828427125 + -2.5 = 0.328427125 y = 0.328427125 Simplifying y = 0.328427125Subproblem 2
y + 2.5 = -2.828427125 Simplifying y + 2.5 = -2.828427125 Reorder the terms: 2.5 + y = -2.828427125 Solving 2.5 + y = -2.828427125 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 = -2.828427125 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -2.828427125 + -2.5 y = -2.828427125 + -2.5 Combine like terms: -2.828427125 + -2.5 = -5.328427125 y = -5.328427125 Simplifying y = -5.328427125Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.328427125, -5.328427125}
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