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Simplifying 2y2 = 11y + -4 Reorder the terms: 2y2 = -4 + 11y Solving 2y2 = -4 + 11y Solving for variable 'y'. Reorder the terms: 4 + -11y + 2y2 = -4 + 11y + 4 + -11y Reorder the terms: 4 + -11y + 2y2 = -4 + 4 + 11y + -11y Combine like terms: -4 + 4 = 0 4 + -11y + 2y2 = 0 + 11y + -11y 4 + -11y + 2y2 = 11y + -11y Combine like terms: 11y + -11y = 0 4 + -11y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -5.5y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5.5y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -5.5y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5.5y + y2 = 0 + -2 -5.5y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5.5y + y2 = -2 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 = -2 + 7.5625 Reorder the terms: 7.5625 + -5.5y + y2 = -2 + 7.5625 Combine like terms: -2 + 7.5625 = 5.5625 7.5625 + -5.5y + y2 = 5.5625 Factor a perfect square on the left side: (y + -2.75)(y + -2.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (y + -2.75) equal to 2.358495283 and -2.358495283.Subproblem 1
y + -2.75 = 2.358495283 Simplifying y + -2.75 = 2.358495283 Reorder the terms: -2.75 + y = 2.358495283 Solving -2.75 + y = 2.358495283 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 = 2.358495283 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = 2.358495283 + 2.75 y = 2.358495283 + 2.75 Combine like terms: 2.358495283 + 2.75 = 5.108495283 y = 5.108495283 Simplifying y = 5.108495283Subproblem 2
y + -2.75 = -2.358495283 Simplifying y + -2.75 = -2.358495283 Reorder the terms: -2.75 + y = -2.358495283 Solving -2.75 + y = -2.358495283 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 = -2.358495283 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = -2.358495283 + 2.75 y = -2.358495283 + 2.75 Combine like terms: -2.358495283 + 2.75 = 0.391504717 y = 0.391504717 Simplifying y = 0.391504717Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.108495283, 0.391504717}
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