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How do you solve using the completing the square method # x^2+8x-9=0#?

Answer 1

Avery Alexander

Completing the square is designed to give you a perfect square trinomial on the left of an equation.

Get any constants on the right side. #x^2+8x=9#

Add #(b/2)^2=(8/2)^2# to both sides #x^2+8x+16=9+16#

Factor the left. #(x+4)^2=25#

Square root both sides. #(x+4)=+-5#

#x={5-4,-5-4} = {1,-9}#

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Answer 2

Hazel Anglin

To solve x^2 + 8x - 9 = 0 using the completing the square method, follow these steps:

Move the constant term to the other side of the equation: x^2 + 8x = 9.
Add the square of half the coefficient of x to both sides of the equation: x^2 + 8x + (8/2)^2 = 9 + (8/2)^2.
Simplify: x^2 + 8x + 16 = 9 + 16.
Factor the left side of the equation: (x + 4)^2 = 25.
Take the square root of both sides: x + 4 = ±√25.
Solve for x: x + 4 = ±5.
Subtract 4 from both sides: x = -4 ± 5.

So the solutions are x = -4 + 5 = 1 and x = -4 - 5 = -9.

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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.