How do you complete the square of x^2-14x+33=0?

X² - 14x + 33 = 0 is in the form ax² + bx + c = 0. We will need this for the second step.

Subtract 33 from both sides

x² - 14x = - 33

Divide the b term by 2 and then square the result. Then add that to both sides.

- 14 / 2 is - 7. ( - 7) ² = 49. Add that to both sides

x² - 14x + 49 = - 33 + 49

Combine the constants and factor the trinomial

(x - 7) ² = 16

Square root both sides

x - 7 = + / - 4

or

x - 7 = - 4 and x - 7 = 4

You have to place a plus-minus statement because ( - 4) ² and 4² both equal 16.

Now we solve for x in each equation. Add 7 to both sides to isolate our variable.

x = 3 and x = 11