Question

Solve 3x^2-18x+5 by completing the square

Answer 1

3(x-3)^2-22

3x^2-18x+5

1 Move the coefficient of x to the front & write the rest normally

3(x^2-6x+5/3)

2 Divide coefficient of x by 2 squared

3[x^2-6x+(-6/2)^2-(-6/2)^2+5/3]

3 Put the first terms into ( )^2

3[(x-3)^2-9+5/2]

4 Add the last 2 terms

= 3(x-3)^2-22

Answer 2

x = 3 + √(22/3) and x = 3 - √(22/3).

Explanation:

Step 1: Divide both sides by the coefficient of x^2 to get the coefficient of x^2 equal to 1.

3x^2 - 18x + 5 = 0

x^2 - 6x + 5/3 = 0

Step 2: Move the constant term to the right-hand side of the equation.

x^2 - 6x = -5/3

Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation.

x^2 - 6x + 9 = -5/3 + 9

(x - 3)^2 = 22/3

Step 4: Solve for x by taking the square root of both sides of the equation.

x - 3 = ±√(22/3)

x = 3 ± √(22/3)