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Simplifying y2 + y + 2y + 2 = 34 Reorder the terms: 2 + y + 2y + y2 = 34 Combine like terms: y + 2y = 3y 2 + 3y + y2 = 34 Solving 2 + 3y + y2 = 34 Solving for variable 'y'. Reorder the terms: 2 + -34 + 3y + y2 = 34 + -34 Combine like terms: 2 + -34 = -32 -32 + 3y + y2 = 34 + -34 Combine like terms: 34 + -34 = 0 -32 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 3y + 32 + y2 = 0 + 32 Reorder the terms: -32 + 32 + 3y + y2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 3y + y2 = 0 + 32 3y + y2 = 0 + 32 Combine like terms: 0 + 32 = 32 3y + y2 = 32 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 = 32 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 32 + 2.25 Combine like terms: 32 + 2.25 = 34.25 2.25 + 3y + y2 = 34.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (y + 1.5) equal to 5.852349955 and -5.852349955.Subproblem 1
y + 1.5 = 5.852349955 Simplifying y + 1.5 = 5.852349955 Reorder the terms: 1.5 + y = 5.852349955 Solving 1.5 + y = 5.852349955 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 = 5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 5.852349955 + -1.5 y = 5.852349955 + -1.5 Combine like terms: 5.852349955 + -1.5 = 4.352349955 y = 4.352349955 Simplifying y = 4.352349955Subproblem 2
y + 1.5 = -5.852349955 Simplifying y + 1.5 = -5.852349955 Reorder the terms: 1.5 + y = -5.852349955 Solving 1.5 + y = -5.852349955 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 = -5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -5.852349955 + -1.5 y = -5.852349955 + -1.5 Combine like terms: -5.852349955 + -1.5 = -7.352349955 y = -7.352349955 Simplifying y = -7.352349955Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.352349955, -7.352349955}
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