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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 = 4.5 6.25 + -5y + y2 = 4.5 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (y + -2.5) equal to 2.121320344 and -2.121320344.Subproblem 1
y + -2.5 = 2.121320344 Simplifying y + -2.5 = 2.121320344 Reorder the terms: -2.5 + y = 2.121320344 Solving -2.5 + y = 2.121320344 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 = 2.121320344 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 2.121320344 + 2.5 y = 2.121320344 + 2.5 Combine like terms: 2.121320344 + 2.5 = 4.621320344 y = 4.621320344 Simplifying y = 4.621320344Subproblem 2
y + -2.5 = -2.121320344 Simplifying y + -2.5 = -2.121320344 Reorder the terms: -2.5 + y = -2.121320344 Solving -2.5 + y = -2.121320344 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 = -2.121320344 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -2.121320344 + 2.5 y = -2.121320344 + 2.5 Combine like terms: -2.121320344 + 2.5 = 0.378679656 y = 0.378679656 Simplifying y = 0.378679656Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.621320344, 0.378679656}
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