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Simplifying 5y = 16 + -1y2 Solving 5y = 16 + -1y2 Solving for variable 'y'. Reorder the terms: -16 + 5y + y2 = 16 + -1y2 + -16 + y2 Reorder the terms: -16 + 5y + y2 = 16 + -16 + -1y2 + y2 Combine like terms: 16 + -16 = 0 -16 + 5y + y2 = 0 + -1y2 + y2 -16 + 5y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -16 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 5y + 16 + y2 = 0 + 16 Reorder the terms: -16 + 16 + 5y + y2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 5y + y2 = 0 + 16 5y + y2 = 0 + 16 Combine like terms: 0 + 16 = 16 5y + y2 = 16 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 = 16 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 16 + 6.25 Combine like terms: 16 + 6.25 = 22.25 6.25 + 5y + y2 = 22.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (y + 2.5) equal to 4.716990566 and -4.716990566.Subproblem 1
y + 2.5 = 4.716990566 Simplifying y + 2.5 = 4.716990566 Reorder the terms: 2.5 + y = 4.716990566 Solving 2.5 + y = 4.716990566 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 = 4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 4.716990566 + -2.5 y = 4.716990566 + -2.5 Combine like terms: 4.716990566 + -2.5 = 2.216990566 y = 2.216990566 Simplifying y = 2.216990566Subproblem 2
y + 2.5 = -4.716990566 Simplifying y + 2.5 = -4.716990566 Reorder the terms: 2.5 + y = -4.716990566 Solving 2.5 + y = -4.716990566 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 = -4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -4.716990566 + -2.5 y = -4.716990566 + -2.5 Combine like terms: -4.716990566 + -2.5 = -7.216990566 y = -7.216990566 Simplifying y = -7.216990566Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.216990566, -7.216990566}
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