x² + 6x - 4 = 0
This won't factor, so we can either solve this
by completing the square or the quadratic formula:
===============================================
By completing the square
Leave only the terms in x on the left side
x² + 6x = 4
To the side multiply the coefficient of x by 1/2,
the square that result:
6×(1/2) = 3
3² = 9
Add that result, 9, to both sides
x² + 6x + 9 = 4 + 9
Now the left side will factor as a
perfect square.
(x + 3)(x + 3) = 4 + 9
Write the left side as the square of
a binomial and combine terms on the right
(x + 3)² = 13
Take square roots of both sides, remembering
± on the right:
________ __
Ö(x + 3)² = ±Ö13
__
x + 3 = ±Ö13
__
x = -3 ± Ö13
===============================================
By the quadratic formula:
x² + 6x - 4 = 0
compare that to
Ax² + Bx + C = 0
Then A=1, B=6, C=-4
Then we use the quadratic formula:
________
-B ± ÖB² - 4AC
x = ————————————————
2A
Substituting for A, B, and C
_______________
-(6) ± Ö(6)² - 4(1)(-4)
x = —————————————————————————
2(1)
_______
-6 ± Ö36 + 16
x = ————————————————
2
__
-6 ± Ö52
x = ——————————
2
____
-6 ± Ö4·13
x = ————————————
2
__
-6 ± 2Ö13
x = ————————————
2
__
-6 ± 2Ö13
x = ———— ± ——————
2 2
3 1 __
-6 ± 2Ö13
x = ———— ± ——————
2 2
1 1
__
x = -3 ± Ö13
Edwin
