Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x2 – 6x = –8
answers
1 x = 4, –2
2 x = –4, 2
3 x = 4, 2
4 x = –4, –2
To solve the equation by completing the square, we need to rearrange the equation to have the form (x-a)^2 = b.
x^2 - 6x = -8
First, we need to add a term to both sides of the equation to complete the square. To do this, we take half the coefficient of x (-6/2 = -3) and square it (-3)^2 = 9.
x^2 - 6x + 9 = -8 + 9
Next, we simplify the equation.
x^2 - 6x + 9 = 1
Notice that the left side of the equation can be factored as a perfect square: (x-3)^2.
(x-3)^2 = 1
Taking the square root of both sides, we can solve for x.
x-3 = ±√1
x-3 = ±1
Adding 3 to both sides, we get two possible values for x.
x = 3 + 1 = 4
x = 3 - 1 = 2
Therefore, the solution to the equation x^2 - 6x = -8 is x = 4 and x = 2.
The correct answer is option 3: x = 4, 2.