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Simplifying y2 + 3y + -476 = 0 Reorder the terms: -476 + 3y + y2 = 0 Solving -476 + 3y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '476' to each side of the equation. -476 + 3y + 476 + y2 = 0 + 476 Reorder the terms: -476 + 476 + 3y + y2 = 0 + 476 Combine like terms: -476 + 476 = 0 0 + 3y + y2 = 0 + 476 3y + y2 = 0 + 476 Combine like terms: 0 + 476 = 476 3y + y2 = 476 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 476 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 476 + 2.25 Combine like terms: 476 + 2.25 = 478.25 2.25 + 3y + y2 = 478.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 478.25 Calculate the square root of the right side: 21.868927729 Break this problem into two subproblems by setting (y + 1.5) equal to 21.868927729 and -21.868927729.Subproblem 1
y + 1.5 = 21.868927729 Simplifying y + 1.5 = 21.868927729 Reorder the terms: 1.5 + y = 21.868927729 Solving 1.5 + y = 21.868927729 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 21.868927729 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 21.868927729 + -1.5 y = 21.868927729 + -1.5 Combine like terms: 21.868927729 + -1.5 = 20.368927729 y = 20.368927729 Simplifying y = 20.368927729Subproblem 2
y + 1.5 = -21.868927729 Simplifying y + 1.5 = -21.868927729 Reorder the terms: 1.5 + y = -21.868927729 Solving 1.5 + y = -21.868927729 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -21.868927729 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -21.868927729 + -1.5 y = -21.868927729 + -1.5 Combine like terms: -21.868927729 + -1.5 = -23.368927729 y = -23.368927729 Simplifying y = -23.368927729Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.368927729, -23.368927729}
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