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X
- WE WANT TO SOLVE THE QUADRATIC EQUATION 6X SQUARED - X - 15 = 0
USING THE QUADRATIC FORMULA GIVEN HERE IN RED
WHERE "A", B AND C
ARE THE COEFFICIENTS OF THE DEGREE TWO TERM,
THE DEGREE ONE TERM AND THE CONSTANT.
SO LOOKING AT OUR EQUATION,
WE NEED TO RECOGNIZE THAT "A" IS EQUAL TO 6, B IS EQUAL TO -1
AND C IS EQUAL TO -15.
SO NOW WE'LL PERFORM SUBSTITUTION
INTO THE QUADRATIC FORMULA.
SO WE'RE NOT GOING TO PERFORM ANY CALCULATIONS HERE,
WE'RE JUST GOING TO PERFORM THE SUBSTITUTION.
SO I'LL HAVE X = -1
PLUS OR MINUS THE SQUARE ROOT OF -1 SQUARED - 4 x 6 x -15.
THE DENOMINATOR IS 2 x 6.
NOW WE'LL START TO SIMPLIFY.
SO WE'LL HAVE X EQUALS-- THIS IS GOING TO BE POSITIVE 1
PLUS OR MINUS THE SQUARE ROOT OF--
THIS NUMBER UNDERNEATH THE SQUARE ROOT
IS CALLED THE DISCRIMINATE.
WE'LL COME BACK TO THAT IN JUST A MOMENT.
THE DENOMINATOR IS GOING TO BE 12,
AND NOW FOR THE DISCRIMINATE WE'LL HAVE -1 SQUARED, THAT'S 1
AND YOU CAN THINK OF THIS AS -4 x 6 x -15,
THAT'S POSITIVE 360.
SO WE'LL HAVE PLUS 360.
SO WE HAVE X = 1 PLUS OR MINUS THE SQUARE ROOT OF 361
DIVIDED BY 12.
AND I BELIEVE 361 IS A PERFECT SQUARE.
LET'S GO AHEAD AND VERIFY THAT.
SO WE HAVE SECOND X SQUARED 361, AND THIS IS--
THE SQUARE ROOT OF 361 IS EQUAL TO 19.
SO WE HAVE X = 1 +/- 19 DIVIDED BY 12.
NOW WE DO WANT TO LIST THE TWO SOLUTIONS.
SO NOW WE'LL PERFORM THIS ADDITION AND SUBTRACTION
AND THEN SIMPLIFY IF NEEDED.
SO ONE SOLUTION WILL BE X = 1 + 19 DIVIDED BY 12.
1 + 19 = 20.
SO WE HAVE 20/12.
WELL, THE GREATEST COMMON FACTOR HERE WOULD BE 4,
SO WE CAN DIVIDED THEM BOTH BY 4.
SO ONE SOLUTION IS 5/3 OR X COULD EQUAL 1 - 19,
WHICH IS -18 DIVIDED BY 12.
THE GREATEST COMMON FACTOR HERE IS 6.
SO WE DIVIDE THEM BOTH BY 6.
THIS WOULD SIMPLIFY TO -3/2.
SO NOTICE HOW WE HAVE TWO REAL RATIONAL SOLUTIONS,
WHICH DOES TELL US THAT THE ORIGINAL EQUATION
WAS FACTORABLE.
OKAY, WE'LL LOOK AT SOME MORE EXAMPLES IN THE NEXT VIDEO.