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Simplifying 2y2 + -13y + 2 + -1y2 + -8y + 16 = 0 Reorder the terms: 2 + 16 + -13y + -8y + 2y2 + -1y2 = 0 Combine like terms: 2 + 16 = 18 18 + -13y + -8y + 2y2 + -1y2 = 0 Combine like terms: -13y + -8y = -21y 18 + -21y + 2y2 + -1y2 = 0 Combine like terms: 2y2 + -1y2 = 1y2 18 + -21y + 1y2 = 0 Solving 18 + -21y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -21y + -18 + y2 = 0 + -18 Reorder the terms: 18 + -18 + -21y + y2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -21y + y2 = 0 + -18 -21y + y2 = 0 + -18 Combine like terms: 0 + -18 = -18 -21y + y2 = -18 The y term is -21y. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21y + 110.25 + y2 = -18 + 110.25 Reorder the terms: 110.25 + -21y + y2 = -18 + 110.25 Combine like terms: -18 + 110.25 = 92.25 110.25 + -21y + y2 = 92.25 Factor a perfect square on the left side: (y + -10.5)(y + -10.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (y + -10.5) equal to 9.604686356 and -9.604686356.Subproblem 1
y + -10.5 = 9.604686356 Simplifying y + -10.5 = 9.604686356 Reorder the terms: -10.5 + y = 9.604686356 Solving -10.5 + y = 9.604686356 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = 9.604686356 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = 9.604686356 + 10.5 y = 9.604686356 + 10.5 Combine like terms: 9.604686356 + 10.5 = 20.104686356 y = 20.104686356 Simplifying y = 20.104686356Subproblem 2
y + -10.5 = -9.604686356 Simplifying y + -10.5 = -9.604686356 Reorder the terms: -10.5 + y = -9.604686356 Solving -10.5 + y = -9.604686356 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = -9.604686356 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = -9.604686356 + 10.5 y = -9.604686356 + 10.5 Combine like terms: -9.604686356 + 10.5 = 0.895313644 y = 0.895313644 Simplifying y = 0.895313644Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.104686356, 0.895313644}
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