Completing the Square Method to Solve Quadratic Equations

Completing the square is a method used to solve quadratic equations by turning them into a perfect square trinomial. Here are the steps to solve 9x^2-15x+6=0 using completing the square method:

Step 1: Divide the coefficient of x^2

The first step is to divide the coefficient of x^2, which is 9 in this case, by 2.

9/2 = 4.5

Step 2: Square the result of step 1

The second step is to square the result of step 1, which is 4.5 in this case.

4.5^2 = 20.25

Step 3: Add and subtract the result of step 2 inside the parentheses

The third step is to add and subtract the result of step 2, which is 20.25, inside the parentheses of the quadratic equation.

9x^2 - 15x + 20.25 - 20.25 + 6 = 0

Step 4: Group the first three terms and factor the perfect square trinomial

The fourth step is to group the first three terms and factor the perfect square trinomial.

(3x - 2.5)^2 - 20.25 + 6 = 0

Step 5: Simplify and solve for x

The fifth and final step is to simplify the equation and solve for x.

(3x - 2.5)^2 - 14.25 = 0

(3x - 2.5)^2 = 14.25

3x - 2.5 = ±√14.25

3x = 2.5 ± √14.25

x = (2.5 ± √14.25)/3

Therefore, the solutions of the quadratic equation 9x^2-15x+6=0 are (2.5 + √14.25)/3 and (2.5 - √14.25)/3.

9x2-15x+6
9x2-9x-6x+6
9x(x-1)-6(x-1)
x=1 andx=6/9 or 2/3