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Simplifying y2 + 3y = 7 Reorder the terms: 3y + y2 = 7 Solving 3y + y2 = 7 Solving for variable 'y'. Reorder the terms: -7 + 3y + y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 3y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + 3y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3y + y2 = 0 + 7 3y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 3y + y2 = 7 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 = 7 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + 3y + y2 = 9.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (y + 1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
y + 1.5 = 3.041381265 Simplifying y + 1.5 = 3.041381265 Reorder the terms: 1.5 + y = 3.041381265 Solving 1.5 + y = 3.041381265 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 = 3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 3.041381265 + -1.5 y = 3.041381265 + -1.5 Combine like terms: 3.041381265 + -1.5 = 1.541381265 y = 1.541381265 Simplifying y = 1.541381265Subproblem 2
y + 1.5 = -3.041381265 Simplifying y + 1.5 = -3.041381265 Reorder the terms: 1.5 + y = -3.041381265 Solving 1.5 + y = -3.041381265 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 = -3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -3.041381265 + -1.5 y = -3.041381265 + -1.5 Combine like terms: -3.041381265 + -1.5 = -4.541381265 y = -4.541381265 Simplifying y = -4.541381265Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.541381265, -4.541381265}
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