- WE WANT TO SOLVE
THE QUADRATIC EQUATION,
X SQUARED + 8X - 16 = 0
USING THE QUADRATIC FORMULA
PROVIDED HERE IN RED
WHERE "A", B AND C
ARE THE COEFFICIENTS
OF THE DEGREE TWO TERM,
THE DEGREE ONE TERM
AND THE CONSTANT.
SO FOR OUR EQUATION,
WE NEED TO RECOGNIZE
THAT "A" IS EQUAL TO 1,
B IS EQUAL TO POSITIVE 8
AND C IS EQUAL TO -16
BECAUSE OF THE SUBTRACTION.
AND NOW WE'LL START BY
PERFORMING THE SUBSTITUTION
INTO THE QUADRATIC FORMULA.
SO WE WOULD HAVE X = -8
PLUS OR MINUS THE SQUARE ROOT
OF 8 SQUARED - 4 x 1 x -16
ALL OVER 2 x 1.
AND NOW WE'LL START TO SIMPLIFY.
WE'LL HAVE X = -8 PLUS OR MINUS
THE SQUARE ROOT OF--
8 SQUARED IS 64
AND WE CAN THINK OF THIS AS
-4 x 1 x -16,
WHICH WOULD BE POSITIVE 64.
SO WE HAVE PLUS 64,
ALL OVER 2 x 1,
WHICH IS EQUAL TO 2.
SO WE HAVE X = -8 PLUS OR MINUS
THE SQUARE ROOT OF--
64 + 64 EQUALS 128,
ALL OVER 2.
NOW THE NEXT STEP IS TO SIMPLIFY
THE SQUARE ROOT OF 128.
THE SQUARE ROOT OF 128 IS EQUAL
TO THE SQUARE ROOT OF 64 x 2,
AND 64 IS A PERFECT SQUARE
SO THIS SIMPLIFIES TO
8 SQUARE ROOT OF 2.
SO WE CAN WRITE THIS AS X =
-8 +/- 8 SQUARE ROOT 2
DIVIDED BY 2,
AND NOW WE NEED TO BE CAREFUL
SIMPLIFYING THIS.
WE CANNOT JUST SIMPLIFY
THE 8 AND THE 2 HERE,
BECAUSE WE'RE DIVIDING
BY A MONOMIAL,
WE CAN WRITE THIS AS
TWO SEPARATE FRACTIONS,
-8 DIVIDED BY 2 +/- 8
SQUARE ROOT 2 DIVIDED BY 2.
SO WE HAVE -8 DIVIDED BY 2 = -4
AND HERE WE HAVE 8 DIVIDED BY 2
AND THAT WOULD BE
+/- 4 SQUARE ROOT 2.
SO WE HAVE TWO REAL IRRATIONAL
SOLUTIONS.
ONE SOLUTION IS X =
-4 + 4 SQUARE ROOT 2
OR X = -4 - 4 SQUARE ROOT 2.
SO BECAUSE WE HAVE TWO REAL
IRRATIONAL SOLUTIONS,
WE COULD NOT HAVE SOLVED THIS
EQUATION BY FACTORING.
WE'LL TAKE A LOOK AT ANOTHER
EXAMPLE IN THE NEXT VIDEO.
