solve the equation by completing the square. if necessary, round to the nearest hundreth.
x^2-18x=19
a ) 1; 19
b ) -1; 19
c ) 3; 6
d ) -3; 1
To solve the equation by completing the square, first rearrange the equation to have the constant term on the right side:
x^2 - 18x = 19
Next, take half of the coefficient of x (-18) and square it:
(-18/2)^2 = 9^2 = 81
Add this value to both sides of the equation:
x^2 - 18x + 81 = 19 + 81
x^2 - 18x + 81 = 100
Now, factor the left side of the equation as a perfect square:
(x - 9)^2 = 100
Take the square root of both sides:
x - 9 = ±√100
x - 9 = ±10
Solve for x by adding 9 to both sides:
x = 9 ± 10
This gives two possible solutions:
x = 19 or x = -1
Therefore, the answer is:
b) -1; 19