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Simplifying y2 + 18y + 43 = 0 Reorder the terms: 43 + 18y + y2 = 0 Solving 43 + 18y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 18y + -43 + y2 = 0 + -43 Reorder the terms: 43 + -43 + 18y + y2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 18y + y2 = 0 + -43 18y + y2 = 0 + -43 Combine like terms: 0 + -43 = -43 18y + y2 = -43 The y term is 18y. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18y + 81 + y2 = -43 + 81 Reorder the terms: 81 + 18y + y2 = -43 + 81 Combine like terms: -43 + 81 = 38 81 + 18y + y2 = 38 Factor a perfect square on the left side: (y + 9)(y + 9) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (y + 9) equal to 6.164414003 and -6.164414003.Subproblem 1
y + 9 = 6.164414003 Simplifying y + 9 = 6.164414003 Reorder the terms: 9 + y = 6.164414003 Solving 9 + y = 6.164414003 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = 6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + y = 6.164414003 + -9 y = 6.164414003 + -9 Combine like terms: 6.164414003 + -9 = -2.835585997 y = -2.835585997 Simplifying y = -2.835585997Subproblem 2
y + 9 = -6.164414003 Simplifying y + 9 = -6.164414003 Reorder the terms: 9 + y = -6.164414003 Solving 9 + y = -6.164414003 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = -6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + y = -6.164414003 + -9 y = -6.164414003 + -9 Combine like terms: -6.164414003 + -9 = -15.164414003 y = -15.164414003 Simplifying y = -15.164414003Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.835585997, -15.164414003}
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