Question

round to the nearest hundredth. solve by completing the square.
x^2+10x=18

Answer 1

To complete the square, we need to add and subtract the square of half of the coefficient of x:

x^2 + 10x = 18
x^2 + 10x + 25 - 25 = 18
(x + 5)^2 - 25 = 18
(x + 5)^2 = 43
x + 5 = ±√43
x = -5 ± √43

Now we can round to the nearest hundredth:

x ≈ -5 + 6.56 ≈ 1.56
or
x ≈ -5 - 6.56 ≈ -11.56

Therefore, the solutions rounded to the nearest hundredth are x ≈ 1.56 and x ≈ -11.56.

Answer 2

To complete the square, we need to add and subtract the square of half of the coefficient of x:

x^2 + 10x = 18
x^2 + 10x + 25 - 25 = 18
(x + 5)^2 - 25 = 18
(x + 5)^2 = 43
x + 5 = ±√43
x = -5 ± √43

Now we can round to the nearest hundredth:

x ≈ -5 + 6.56 ≈ 1.56
or
x ≈ -5 - 6.56 ≈ -11.56

Therefore, the solutions rounded to the nearest hundredth are x ≈ 1.56 and x ≈ -11.56.

Answer 3

That's correct! Good job!