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Simplifying 2y2 + -21y + 8 = 0 Reorder the terms: 8 + -21y + 2y2 = 0 Solving 8 + -21y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -10.5y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10.5y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -10.5y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10.5y + y2 = 0 + -4 -10.5y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10.5y + y2 = -4 The y term is -10.5y. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5y + 27.5625 + y2 = -4 + 27.5625 Reorder the terms: 27.5625 + -10.5y + y2 = -4 + 27.5625 Combine like terms: -4 + 27.5625 = 23.5625 27.5625 + -10.5y + y2 = 23.5625 Factor a perfect square on the left side: (y + -5.25)(y + -5.25) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (y + -5.25) equal to 4.85412196 and -4.85412196.Subproblem 1
y + -5.25 = 4.85412196 Simplifying y + -5.25 = 4.85412196 Reorder the terms: -5.25 + y = 4.85412196 Solving -5.25 + y = 4.85412196 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + y = 4.85412196 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + y = 4.85412196 + 5.25 y = 4.85412196 + 5.25 Combine like terms: 4.85412196 + 5.25 = 10.10412196 y = 10.10412196 Simplifying y = 10.10412196Subproblem 2
y + -5.25 = -4.85412196 Simplifying y + -5.25 = -4.85412196 Reorder the terms: -5.25 + y = -4.85412196 Solving -5.25 + y = -4.85412196 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + y = -4.85412196 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + y = -4.85412196 + 5.25 y = -4.85412196 + 5.25 Combine like terms: -4.85412196 + 5.25 = 0.39587804 y = 0.39587804 Simplifying y = 0.39587804Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.10412196, 0.39587804}
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