9514 1404 393
Answer:
- x = ±√13
- x = ±3√6
- x = ±√66
- x = 0 or 8
Step-by-step explanation:
As in any "solve for" situation, you "undo" what is done to the variable.
Here, (for 3 of the 4 problems) the variable is ...
- squared
- multiplied by a constant
- added to a constant
We undo these operations in reverse order. First, we add the opposite of the added constant. Then we divide by the coefficient of x². Finally, we take the square root to "undo" the squaring operation.
1. 4x² -30 = 22 . . . . . . given
4x² = 52 . . . . . . . . . add 30 to both sides
x² = 13 . . . . . . . . . . . divide both sides by 4
x = ±√13 . . . . . . . . . take the square root. Both signs are solutions.
__
2. 3x² +4 = 166 . . . . . given
3x² = 162 . . . . . . . . add -4 to both sides
x² = 54 . . . . . . . . . . divide both sides by 3
x = ±√54 . . . . . . . . take the square root. 54 = 3²·6 has a square factor
x = ±3√6 . . . . . . . simplified result
__
3. (1/3)x² +14 = 36 . . . . given
(1/3)x² = 22 . . . . . . . . add -14 to both sides
x² = 66 . . . . . . . . . . . multiply both sides by 3
x = ±√66 . . . . . . . . take the square root
__
4. The same "undo" idea applies. Here, we can start with the square root.
(x -4)² = 16 . . . . . given
x -4 = ±4 . . . . . . . square root
x = 4 ± 4 . . . . . . add 4 to both sides
This means x = 4-4 = 0, or x = 4+4 = 8.
The solutions are x = 0, x = 8.
