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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.
<span>3. x^2+6x =16
-------------------------
(6/2)^2 = 9
x</span>² + 6x + 9 = 16 + 9
(x + 3)² = 25
<span>4. x^2-10x =11
------------------------
(-10/2)</span>² = 25
x² - 10x + 25 = 11 + 25
(x -5)² = 36
<span>5. x^2-9x =0
--------------
(-9/2)</span>² = 81/4
x² - 9x + 81/4 = 81/4
(x - 9/2)² = 81/4
<span>6. x^2+16x =15
---------------
(16/2)</span>² = 64
x² + 16x +64 = 15 + 64
(x + 8)² = 79
<span>7. 3x^2+18x-81=0
----------------
x</span>² + 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:
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
<span>3. x^2+6x =16
-------------------------
(6/2)^2 = 9
x</span>² + 6x + 9 = 16 + 9
(x + 3)² = 25
<span>4. x^2-10x =11
------------------------
(-10/2)</span>² = 25
x² - 10x + 25 = 11 + 25
(x -5)² = 36
<span>5. x^2-9x =0
--------------
(-9/2)</span>² = 81/4
x² - 9x + 81/4 = 81/4
(x - 9/2)² = 81/4
<span>6. x^2+16x =15
---------------
(16/2)</span>² = 64
x² + 16x +64 = 15 + 64
(x + 8)² = 79
<span>7. 3x^2+18x-81=0
----------------
x</span>² + 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:
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