Solve the equation by completing the square. If necessary, round to the nearest hundredth.
x² – 18x = 19
(1 point)
Responses
1; 19
1; 19
–1; 19
–1; 19
3; 6
3; 6
–3; 1
To solve this equation by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation.
x² – 18x = 19 is equivalent to x² – 18x - 19 = 0.
Step 2: To complete the square, divide the coefficient of x by 2 and square the result.
-18/2 = -9, (-9)² = 81.
Step 3: Add and subtract this squared value inside the parentheses.
x² – 18x + 81 - 81 - 19 = 0.
(x - 9)² = 100.
Step 4: Take the square root of both sides.
x - 9 = ±√100.
x - 9 = ±10.
Step 5: Solve for x.
x = 9 ± 10.
So, the solutions are x = 19 and x = -1. Rounding to the nearest hundredth, x = 19 and x = -1 are equivalent to x = 19.00 and x = -1.00.
The correct response is:
1; 19