3x^2+8x-3=0 complete the square?

x= 1/3 , -3

1)divide out by 3 on both sides to set the leading coeff. to 1

3x²+8x-3=0

---------------

3

= x²+8/3x-1=0

2)Add 1 to both sides

x²+8/3x-1=0

+1 +1

=x²+8/3x=1

3)Figure the following on the side:

b=8/3

½b=4/3

(½b)²=16/9

4) use the results to complete the square by adding 16/9 to both sides.

x²+8/3x = 1

+16/9 +16/9

=x²+8/3x +16/9 = 25/9

5) convert the new polynomial back to an equal squared binomial.

x²+8/3x +16/9 = 25/9

(x+4/3)² =25/9

6)take the square root of both sides. (dont for get the plus minus on the answer side!)

√ (x+4/3)² =±√ 25/9

simplify.

x+4/3 = ± 5/3

7)solve for both x's

x+4/3 = 5/3

-4/3

x=1/3

x+4/3 = - 5/3

-4/3

x=-3

a million) x^2+8x= -15 then you definitely could discover: (b/2)^2 using fact the answer to this formulation will supply you the variety that makes a suitable sq. trinomial. (8/2)^2= sixteen then: you may upload sixteen to the two facets. x^2+8x+sixteen= -15+sixteen this is now straight forward to element the suitable sq. trinomial. (x+4)^2= a million with the intention to isolate the x, you may choose to first sq. root the a million which delivers: x+4= +/-a million subtract 4 from the two facets for the two suggestions: x= -a million-4= -5 x= a million-4= -3 this is the variety you finished the sq.. the tactic the guy above me used became factorizing. i do no longer choose to remedy the rest for you using fact i could be depriving you of getting to know the thank you to get the solutions your self.

3x^2+8x-3 = 3 ( x^2 + 8/3 x + 16/9) - 16/3 - 3

= 3 ( x + 4/3)^2 - 25/3 = 0

So (x + 4/3)^2 = 25/9

So (x + 4/3) = (+/-) (5/3)

either x = 5/3 - 4/3 = 1/3

or x = 5/3 + 4/3 = 9/3 = 3

ax^2+bx+c=0

divide by 3

x^2 + (8/3)x -1 =0

add (b/2)^2 in both sides

x^2+(8/3)x-1+ (16/9) - (16/9)=0

(x+16/9)^2-25/9=0

.....

OR from begaining

(3x-1)(x+3)=0

3x^2+8x-3=0

(3x-1)(x+3)

x=1/3 or -3

3x^2+8x-3=0

(3x-1)(x+3)=0

x= 1/3 or -3

3x^2 - 9x + x - 3 = 0

3x(x - 3) + 1(x - 3) = 0

(3x + 1)(x - 3) = 0

3x/3 = -1/3

x = -1/3 or x = 3

x=3,1/3