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Raphael Foster
Mathematics
22 September, 01:24
How do you complete the square of x^2-14x+33=0?
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Natalya Farley
22 September, 01:43
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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
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