Question

Complete the square
x²-8x-65=0

Answer 1

x=-5 and x=13

Step-by-step explanation:

Given equation is:

$x^2-8x-65=0$

Adding 65 to both sides

$x^2-8x-65+65=0+65\\x^2-8x=65$

Now to decide what to add

$8x = 2ab\\8x=2.x.b\\\frac{8x}{2x} = b\\b=4$

So we will add (4)^2 to both sides

$x^2-8x+(4)^2=65+(4)^2\\Using\ formula: (a^2-2ab+b^2)=(a-b)^2\\(x-4)^2=65+16\\(x-4)^2=81Taking\ square\ root\ on\ both\ sides\\\sqrt{(x-4)^2}=\sqrt{81}\\x-4=-9\ \ \ \ and\ x-4=9\\x=-9+4\ \ \ \ and\ \ \ x=9+4\\x=-5,\ x=13$

So the solution is:

x=-5 and x=13

Keywords: Completing Square, Variables

Learn more about quadratic equations at:

• brainly.com/question/13063819
• brainly.com/question/13219835

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