X^2-6x-10=0 find the perfect square

Answer 1

To find the perfect square of this equation, you can try completing the square. First, add 10 to both sides to get:

x^2 - 6x = 10

Next, take half of the coefficient of x (-6) and square it. Half of -6 is -3, and (-3)^2 is 9. Add 9 to both sides:

x^2 - 6x + 9 = 19

The left side of the equation is now a perfect square, specifically (x - 3)^2. Rewrite the equation:

(x - 3)^2 = 19

And take the square root of both sides:

x - 3 = ±√19

Finally, solve for x by adding 3 to both sides:

x = 3 ± √19

So the perfect square in this equation is (x - 3)^2.