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Simplifying y2 + 7y + 10 = 30 Reorder the terms: 10 + 7y + y2 = 30 Solving 10 + 7y + y2 = 30 Solving for variable 'y'. Reorder the terms: 10 + -30 + 7y + y2 = 30 + -30 Combine like terms: 10 + -30 = -20 -20 + 7y + y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -20 + 7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 7y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + 7y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 7y + y2 = 0 + 20 7y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 7y + y2 = 20 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = 20 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 20 + 12.25 Combine like terms: 20 + 12.25 = 32.25 12.25 + 7y + y2 = 32.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (y + 3.5) equal to 5.678908346 and -5.678908346.Subproblem 1
y + 3.5 = 5.678908346 Simplifying y + 3.5 = 5.678908346 Reorder the terms: 3.5 + y = 5.678908346 Solving 3.5 + y = 5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 5.678908346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 5.678908346 + -3.5 y = 5.678908346 + -3.5 Combine like terms: 5.678908346 + -3.5 = 2.178908346 y = 2.178908346 Simplifying y = 2.178908346Subproblem 2
y + 3.5 = -5.678908346 Simplifying y + 3.5 = -5.678908346 Reorder the terms: 3.5 + y = -5.678908346 Solving 3.5 + y = -5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -5.678908346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -5.678908346 + -3.5 y = -5.678908346 + -3.5 Combine like terms: -5.678908346 + -3.5 = -9.178908346 y = -9.178908346 Simplifying y = -9.178908346Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.178908346, -9.178908346}
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