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Simplifying y2 + y = 9 Reorder the terms: y + y2 = 9 Solving y + y2 = 9 Solving for variable 'y'. Reorder the terms: -9 + y + y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + y + y2 = 0 + 9 y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 y + y2 = 9 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = 9 + 0.25 Reorder the terms: 0.25 + y + y2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + y + y2 = 9.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (y + 0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
y + 0.5 = 3.041381265 Simplifying y + 0.5 = 3.041381265 Reorder the terms: 0.5 + y = 3.041381265 Solving 0.5 + y = 3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.041381265 + -0.5 y = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 y = 2.541381265 Simplifying y = 2.541381265Subproblem 2
y + 0.5 = -3.041381265 Simplifying y + 0.5 = -3.041381265 Reorder the terms: 0.5 + y = -3.041381265 Solving 0.5 + y = -3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.041381265 + -0.5 y = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 y = -3.541381265 Simplifying y = -3.541381265Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.541381265, -3.541381265}
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