Solve a quadratic equation through completing the square
Now it's time to see how we employ completing the square to solve out a quadratic equation. The procedure is best seen as we work an instance thus let's do that.
Example: By using complete the square method to solve each of the following quadratic equations.
x^{2} - 6x + 1 = 0
Solution
x^{2} - 6x + 1 = 0
Step 1 : Divide the equation through the coefficient of the x^{2} term. Remember that completing the square needed a coefficient of one on this term & it will guarantee that we will get that. However, we don't need doing that for this equation.
Step 2 : Set the equation up in order that the x's are on the left side & the constant is on the right side.
x^{2} - 6x = -1
Step 3: Complete the square on the left side. Though, this time we will have to add the number to both sides of the equal sign rather than just the left side. It is because we have to recall the rule that what we do to one side of an equation we have to do to the other side of the equation.
First one, here is the number we adding up to both sides.
( -6/ 2 )^{ 2}= (-3)^{2 }= 9
Now, complete the square.
x^{2} - 6x + 9 = -1 +9
(x - 3)^{2 }= 8
Step 4: Now, at this instance notice that we can employ the square root property on this equation. That was the reason of the first three steps. Doing this will provides us the solution to the equation.
x - 3 = ± 8 ⇒ x = 3 ± √8
And i.e. the procedure. Let's now do the remaining parts.