2007-12-02 13:26:22 · 3 answers · asked by Jay 1 in Science & Mathematics ➔ Mathematics
solve for x by completing the square: -6x = 3x^2 – 2. Sorry it's 3x to the 2nd power.
2007-12-02 13:27:22 · update #1
here are the answers I have to choose from:
a. –3 3 / 3
b. [–3 (15)1/2 ]/ 3
c. 3 3 / 3
d. [3 (15)1/2 ]/ 3
2007-12-02 13:43:47 · update #2
a. –3 +- sqrt3 / 3
b. [–3 +- (15)1/2 ]/ 3
c. 3 +- sqrt3 / 3
d. [3 +- (15)1/2 ]/ 3
sorry it didn't like the characters...
2007-12-02 13:46:03 · update #3
- 6x = 3x² -2 Taking -6x and -2 to the other side we get
3x²+6x = 2 Divide the entire equation with the coefficient of x² ie: 3
x² + 6/3x = 2/3
x²+2x = 2/3 add the square of one half of the coefficient of x on either side to complete the square
one half of 2 = 1 and square of 1 is 1 , adding 1 to both sides
x²+2x+1 = 2/3+1 now the equation on the left hand side is of the form (x+c)²
(x+1)² = 5/3 Taking square root on both sides
x+1 = √5/3 There are two roots , the negative root and the positive root which form the roots ie: (a)² = a² and (-a)² is also a²
x = √5/√3 - 1
x = -√5/√3 -1
2007-12-02 13:39:13 · answer #1 · answered by A Little Sarcasm Helps 5 · 0⤊ 0⤋
-6x = 3x^2 - 2
Get the constant term by itself on the left...
2 = 3x^2 + 6x
Divide through by the coefficient on x^2 ( that is, by three)...
2/3 = x^2 + 2x
Add the square of the coefficient of x (four) to both sides to complete the square...
2/3 + 4 = x^2 + 2x + 4
Simplify on the left, factor on the right...
14 / 4 = ( x + 2 )^2
Done! Now you can take the square root of both sides to get
sqrt ( 14 ) / 2 = x + 2
and solve for x
2007-12-02 21:38:32 · answer #2 · answered by jgoulden 7 · 0⤊ 1⤋
3x^2 -6x= 2
x^2 -2x = 2/3
x^2 -2x +1 = (2/3) + 1
(x-1)^2 = 5/3
x-1 = ± sqrt(5/3)
x = ± sqrt(5/3) +1
2007-12-02 21:40:28 · answer #3 · answered by pikester666 3 · 0⤊ 0⤋