use the square root property to find all solutions of x^2+10x+25=81

Answer 1

We can write the given equation in its factored form as:

(x+5)² = 81

Take the square root of both sides and:

x + 5 = 9

x + 5 = -9

So, x = 4 or x = -14.

Checking these values shows that both are correct solutions.

Note: if you solve this type of problem for the general case, you derive the quadratic formula. And the method demonstrated is a special case of "completing the square".

Answer 2

(x+5)^2 =9^2

x+5=+/-9

x= -14 or 4

check the answers:

x^2 +10x +25= 81

4^2 +10(4)+25=16+40+25= 81

(-14)^2 +10(-14) +25 = 196-140+25 = 81