To complete the square, we need to add a constant term to both sides of the equation that will allow us to write the left side as a perfect square trinomial. We can determine this constant term by taking half of the coefficient of x, squaring it, and adding it to both sides.
- First, let's take half of the coefficient of x:
-6/2 = -3
- Now let's square it:
(-3)^2 = 9
- Finally, let's add 9 to both sides of the equation:
x^2 - 6x + 7 + 9 = 9
- Simplifying the left side:
(x - 3)^2 = 2
- Taking the square root of both sides:
x - 3 = ±√2
- Adding 3 to both sides:
x = 3 ± √2
The solution is x = 3 ± √2.
solve the equation by completing the square
x^2-6x+7=0
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