How do you solve using the completing the square method #y^2 + 16y = 2#?

Answer 1

#y = -8 +- sqrt66#

find the number needed to complete the square: #(b/2)^2 = (16/2)^2 = 64# add to both sides of w=equation #y^2 + 16y + 64 = 2 + 64# factor and simplify #(y + 8)(y + 8) = 66 -> (y + 8)^2 = 66# take square root of both sides #y + 8 = +- sqrt66# subtract 8 from both sides #y = -8 +-sqrt66#

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Answer 2

Eva Abramson

To solve the equation using the completing the square method, follow these steps:

Rewrite the equation: (y^2 + 16y = 2).
Move the constant term to the other side of the equation: (y^2 + 16y - 2 = 0).
To complete the square, take half of the coefficient of (y) (which is 16), square it, and add it to both sides of the equation: (y^2 + 16y + 64 = 2 + 64).
Simplify: (y^2 + 16y + 64 = 66).
Factor the left side: ((y + 8)^2 = 66).
Take the square root of both sides: (y + 8 = \pm \sqrt{66}).
Solve for (y): (y = -8 \pm \sqrt{66}).

So, the solutions are (y = -8 + \sqrt{66}) and (y = -8 - \sqrt{66}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.