Pls help me also show your work bc I need to understand

9514 1404 393

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 ...

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.

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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

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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

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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.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."