Question

Solve each equation by completing the square. round to the nearest hundredth if necessary.

3. x^2+6x =16
4. x^2-10x =11
5. x^2-9x =0
6. x^2+16x =15
7. 3x^2+18x-81=0
use the quadratic formula to solve each equation. round to the nearest hundredth if necessary.
8. 4x^2+3x-8=0
9.2x^2-7x+3=0
10. x^2-2x+3=0
11. 2x^2+4x-7=0

Answer 1

3. -8,2
4. -1,11
5. 0,9
6. -16.89, 0.89
7. -9,3
8. -1.84, 1.09

Answer 2

To comlete each square, you just have to take the middle term and divide it by 2, then take its square. Add this to both sides of the equation then simplify. The middle term is the 1st degree x variable.

3. x^2+6x =16
-------------------------
(6/2)^2 = 9
x² + 6x + 9 = 16 + 9
(x + 3)² = 25

4. x^2-10x =11
------------------------
(-10/2)² = 25
x² - 10x + 25 = 11 + 25
(x -5)² = 36

5. x^2-9x =0
--------------
(-9/2)² = 81/4
x² - 9x + 81/4 = 81/4
(x - 9/2)² = 81/4

6. x^2+16x =15
---------------
(16/2)² = 64
x² + 16x +64 = 15 + 64
(x + 8)² = 79

7. 3x^2+18x-81=0
----------------
x² + 6x = 27
(6/2)² = 9
x² + 6x + 9 = 27 + 9
(x + 3)² = 36

A polynomial with a general equation of ax² + bx + c = 0 has a root determined using this formula:


`x= \frac{-b \ +/- \ \sqrt{ b^(2)-4ac } }{2a}`

Just substitute the coefficients to the formula to find the roots

8. 1.09, -1.84
9. 3, 1/2
10. No real roots
11. 1.12, -3.12