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Simplifying 7y2 + -33y + -480 = 0 Reorder the terms: -480 + -33y + 7y2 = 0 Solving -480 + -33y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -68.57142857 + -4.714285714y + y2 = 0 Move the constant term to the right: Add '68.57142857' to each side of the equation. -68.57142857 + -4.714285714y + 68.57142857 + y2 = 0 + 68.57142857 Reorder the terms: -68.57142857 + 68.57142857 + -4.714285714y + y2 = 0 + 68.57142857 Combine like terms: -68.57142857 + 68.57142857 = 0.00000000 0.00000000 + -4.714285714y + y2 = 0 + 68.57142857 -4.714285714y + y2 = 0 + 68.57142857 Combine like terms: 0 + 68.57142857 = 68.57142857 -4.714285714y + y2 = 68.57142857 The y term is -4.714285714y. Take half its coefficient (-2.357142857). Square it (5.556122448) and add it to both sides. Add '5.556122448' to each side of the equation. -4.714285714y + 5.556122448 + y2 = 68.57142857 + 5.556122448 Reorder the terms: 5.556122448 + -4.714285714y + y2 = 68.57142857 + 5.556122448 Combine like terms: 68.57142857 + 5.556122448 = 74.127551018 5.556122448 + -4.714285714y + y2 = 74.127551018 Factor a perfect square on the left side: (y + -2.357142857)(y + -2.357142857) = 74.127551018 Calculate the square root of the right side: 8.609735827 Break this problem into two subproblems by setting (y + -2.357142857) equal to 8.609735827 and -8.609735827.Subproblem 1
y + -2.357142857 = 8.609735827 Simplifying y + -2.357142857 = 8.609735827 Reorder the terms: -2.357142857 + y = 8.609735827 Solving -2.357142857 + y = 8.609735827 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + y = 8.609735827 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + y = 8.609735827 + 2.357142857 y = 8.609735827 + 2.357142857 Combine like terms: 8.609735827 + 2.357142857 = 10.966878684 y = 10.966878684 Simplifying y = 10.966878684Subproblem 2
y + -2.357142857 = -8.609735827 Simplifying y + -2.357142857 = -8.609735827 Reorder the terms: -2.357142857 + y = -8.609735827 Solving -2.357142857 + y = -8.609735827 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + y = -8.609735827 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + y = -8.609735827 + 2.357142857 y = -8.609735827 + 2.357142857 Combine like terms: -8.609735827 + 2.357142857 = -6.25259297 y = -6.25259297 Simplifying y = -6.25259297Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.966878684, -6.25259297}
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