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Simplifying (-9.285714286 + 0.5714285714y)(-9.285714286 + 0.5714285714y) + y2 = 65 Multiply (-9.285714286 + 0.5714285714y) * (-9.285714286 + 0.5714285714y) (-9.285714286(-9.285714286 + 0.5714285714y) + 0.5714285714y * (-9.285714286 + 0.5714285714y)) + y2 = 65 ((-9.285714286 * -9.285714286 + 0.5714285714y * -9.285714286) + 0.5714285714y * (-9.285714286 + 0.5714285714y)) + y2 = 65 ((86.2244898 + -5.306122449y) + 0.5714285714y * (-9.285714286 + 0.5714285714y)) + y2 = 65 (86.2244898 + -5.306122449y + (-9.285714286 * 0.5714285714y + 0.5714285714y * 0.5714285714y)) + y2 = 65 (86.2244898 + -5.306122449y + (-5.306122449y + 0.3265306122y2)) + y2 = 65 Combine like terms: -5.306122449y + -5.306122449y = -10.612244898y (86.2244898 + -10.612244898y + 0.3265306122y2) + y2 = 65 Combine like terms: 0.3265306122y2 + y2 = 1.3265306122y2 86.2244898 + -10.612244898y + 1.3265306122y2 = 65 Solving 86.2244898 + -10.612244898y + 1.3265306122y2 = 65 Solving for variable 'y'. Reorder the terms: 86.2244898 + -65 + -10.612244898y + 1.3265306122y2 = 65 + -65 Combine like terms: 86.2244898 + -65 = 21.2244898 21.2244898 + -10.612244898y + 1.3265306122y2 = 65 + -65 Combine like terms: 65 + -65 = 0 21.2244898 + -10.612244898y + 1.3265306122y2 = 0 Begin completing the square. Divide all terms by 1.3265306122 the coefficient of the squared term: Divide each side by '1.3265306122'. 16 + -8y + y2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -8y + -16 + y2 = 0 + -16 Reorder the terms: 16 + -16 + -8y + y2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -8y + y2 = 0 + -16 -8y + y2 = 0 + -16 Combine like terms: 0 + -16 = -16 -8y + y2 = -16 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = -16 + 16 Reorder the terms: 16 + -8y + y2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -8y + y2 = 0 Factor a perfect square on the left side: (y + -4)(y + -4) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (y + -4) equal to 0 and 0.Subproblem 1
y + -4 = 0 Simplifying y + -4 = 0 Reorder the terms: -4 + y = 0 Solving -4 + y = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + y = 0 + 4 y = 0 + 4 Combine like terms: 0 + 4 = 4 y = 4 Simplifying y = 4Subproblem 2
y + -4 = 0 Simplifying y + -4 = 0 Reorder the terms: -4 + y = 0 Solving -4 + y = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + y = 0 + 4 y = 0 + 4 Combine like terms: 0 + 4 = 4 y = 4 Simplifying y = 4Solution
The solution to the problem is based on the solutions from the subproblems. y = {4, 4}
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