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Simplifying 2(y2 + 4) + -11(y + 2) + -21 = 0 Reorder the terms: 2(4 + y2) + -11(y + 2) + -21 = 0 (4 * 2 + y2 * 2) + -11(y + 2) + -21 = 0 (8 + 2y2) + -11(y + 2) + -21 = 0 Reorder the terms: 8 + 2y2 + -11(2 + y) + -21 = 0 8 + 2y2 + (2 * -11 + y * -11) + -21 = 0 8 + 2y2 + (-22 + -11y) + -21 = 0 Reorder the terms: 8 + -22 + -21 + -11y + 2y2 = 0 Combine like terms: 8 + -22 = -14 -14 + -21 + -11y + 2y2 = 0 Combine like terms: -14 + -21 = -35 -35 + -11y + 2y2 = 0 Solving -35 + -11y + 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'. -17.5 + -5.5y + y2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -5.5y + 17.5 + y2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -5.5y + y2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -5.5y + y2 = 0 + 17.5 -5.5y + y2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -5.5y + y2 = 17.5 The y term is -5.5y. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5y + 7.5625 + y2 = 17.5 + 7.5625 Reorder the terms: 7.5625 + -5.5y + y2 = 17.5 + 7.5625 Combine like terms: 17.5 + 7.5625 = 25.0625 7.5625 + -5.5y + y2 = 25.0625 Factor a perfect square on the left side: (y + -2.75)(y + -2.75) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (y + -2.75) equal to 5.006246099 and -5.006246099.Subproblem 1
y + -2.75 = 5.006246099 Simplifying y + -2.75 = 5.006246099 Reorder the terms: -2.75 + y = 5.006246099 Solving -2.75 + y = 5.006246099 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = 5.006246099 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = 5.006246099 + 2.75 y = 5.006246099 + 2.75 Combine like terms: 5.006246099 + 2.75 = 7.756246099 y = 7.756246099 Simplifying y = 7.756246099Subproblem 2
y + -2.75 = -5.006246099 Simplifying y + -2.75 = -5.006246099 Reorder the terms: -2.75 + y = -5.006246099 Solving -2.75 + y = -5.006246099 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = -5.006246099 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = -5.006246099 + 2.75 y = -5.006246099 + 2.75 Combine like terms: -5.006246099 + 2.75 = -2.256246099 y = -2.256246099 Simplifying y = -2.256246099Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.756246099, -2.256246099}
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