Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2 - 4x = 5
To solve the equation by completing the square, we want to manipulate the equation so that its left side can be expressed as a perfect square trinomial.
Starting with x^2 - 4x = 5, we can complete the square by adding and subtracting a constant term to the equation.
First, take the coefficient of x, which is -4, divide it by 2, and square the result:
-4/2 = -2
(-2)^2 = 4
Next, add and subtract this result to the equation:
x^2 - 4x + 4 - 4 = 5
Now, rewrite the equation as:
(x^2 - 4x + 4) - 4 = 5
Simplify the perfect square trinomial on the left side:
(x - 2)^2 - 4 = 5
To isolate the square term, add 4 to both sides:
(x - 2)^2 = 9
Take the square root of both sides (both positive and negative square roots):
x - 2 = ± √9
Simplify:
x - 2 = ± 3
Finally, add 2 to both sides to solve for x:
x = 2 ± 3
The solutions to the equation are:
x = 2 + 3 = 5
x = 2 - 3 = -1