Answer: x = "-1 " ; <u>and</u>: "(1 ± √3) / 2" .
____________________________________________
Explanation:
____________________________________________
Given: 3x³ − 2x + 1 = 0 ; Find "x" ;
Factor: "3x³ − 2x + 1" ;
3x³ − 2x + 1 = (3x² <span>− 3x + 1)(x + 1) ;
Now, set the equation equal to "0" (zero);
</span> (3x² − 3x + 1)(x + 1) = 0 ;
x = 0 ; when:
__________________________________
(x + 1) = 0 ; and/or: when:
(3x² − 3x + 1) = 0 ;
__________________________________
Start with "x + 1 = 0" ;
Subtract "1" from each side of the equation ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;
x + 1 − 1 = 0 − 1 ;
x = -1 ;
_______________________________
Now, try:
3x² − 3x + 1 = 0 ;
Since: "3x² − 3x + 1 " cannot be factored; and since:
"3x² − 3x + 1 = 0" ; is written in the "quadratic equation format"; that is:
"ax² + bx + c = 0 ; a ≠ 0; We can use the "quadratic equation formula" to solve for "x" ;
in which "a = 3" ;
"b = -3" ;
"c = 1" ;
The quadratic equation formula is:
__________________________________
x = [-b ± √(b²−4ac] / 2a ;
= ? (Let us plug in our known values for "a, b, & c"l
x = { [-(-3] ± [√[(-3²) − (4*3*1)] } / {2* 3} ;
x = [3 ± √(9 − 12)] / 6
x = [3 ± √(-3 )] / 6 ;
x = (1 ± √3) / 2 .
<span>__________________________________________________
So, the answers are: x = " -1 " ; and: "</span>(1 ± √3) / 2 " .
__________________________________________________
That is a answer try uploading the question
Your answer would be 28.
We can find this by first forming the equation 3x + 2 = 5x - 6, as P is the midpoint and so DP = PE.
3x + 2 = 5x - 6
- 3x
2 = 2x - 6
+ 6
8 = 2x
÷ 2
x = 4
Now we substitute in 4 when we add together (3x + 2) + (5x - 6), as these two parts make up the whole line:
(3 × 4) + 2 + (5 × 4) - 6 = 12 + 2 + 20 - 6 = 34 - 6 = 28
I hope this helps!
Always make the unknown subject of the equation