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Simplifying y2 + 6.7658y + -18.8548 = 0 Reorder the terms: -18.8548 + 6.7658y + y2 = 0 Solving -18.8548 + 6.7658y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '18.8548' to each side of the equation. -18.8548 + 6.7658y + 18.8548 + y2 = 0 + 18.8548 Reorder the terms: -18.8548 + 18.8548 + 6.7658y + y2 = 0 + 18.8548 Combine like terms: -18.8548 + 18.8548 = 0.0000 0.0000 + 6.7658y + y2 = 0 + 18.8548 6.7658y + y2 = 0 + 18.8548 Combine like terms: 0 + 18.8548 = 18.8548 6.7658y + y2 = 18.8548 The y term is 6.7658y. Take half its coefficient (3.3829). Square it (11.44401241) and add it to both sides. Add '11.44401241' to each side of the equation. 6.7658y + 11.44401241 + y2 = 18.8548 + 11.44401241 Reorder the terms: 11.44401241 + 6.7658y + y2 = 18.8548 + 11.44401241 Combine like terms: 18.8548 + 11.44401241 = 30.29881241 11.44401241 + 6.7658y + y2 = 30.29881241 Factor a perfect square on the left side: (y + 3.3829)(y + 3.3829) = 30.29881241 Calculate the square root of the right side: 5.504435703 Break this problem into two subproblems by setting (y + 3.3829) equal to 5.504435703 and -5.504435703.Subproblem 1
y + 3.3829 = 5.504435703 Simplifying y + 3.3829 = 5.504435703 Reorder the terms: 3.3829 + y = 5.504435703 Solving 3.3829 + y = 5.504435703 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.3829' to each side of the equation. 3.3829 + -3.3829 + y = 5.504435703 + -3.3829 Combine like terms: 3.3829 + -3.3829 = 0.0000 0.0000 + y = 5.504435703 + -3.3829 y = 5.504435703 + -3.3829 Combine like terms: 5.504435703 + -3.3829 = 2.121535703 y = 2.121535703 Simplifying y = 2.121535703Subproblem 2
y + 3.3829 = -5.504435703 Simplifying y + 3.3829 = -5.504435703 Reorder the terms: 3.3829 + y = -5.504435703 Solving 3.3829 + y = -5.504435703 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.3829' to each side of the equation. 3.3829 + -3.3829 + y = -5.504435703 + -3.3829 Combine like terms: 3.3829 + -3.3829 = 0.0000 0.0000 + y = -5.504435703 + -3.3829 y = -5.504435703 + -3.3829 Combine like terms: -5.504435703 + -3.3829 = -8.887335703 y = -8.887335703 Simplifying y = -8.887335703Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.121535703, -8.887335703}
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