10G (2.3) Finding a variable with an exponent

Finding a variable when it has an exponent

​(2.3)

Multiple Choice

$$x^2=9$$

• x = 5 or x = -5
• x = 6 or x = -6
• x = 2 or x = -2
• x = 3 or x = -3
• x = 4 or x = -4

To get rid of a "squared",
you take the square root

Multiple Choice

If $$x^2=9$$

How can x = -3 if my calculator says $$\sqrt[]{9}=3$$ ?

• Because

  $$-3\ \cdot\ -3\ =\ 9$$

• Because -3 and 3 are the same thing

• Because

  $$3\cdot3=-9$$

• Because

  $$-3\cdot-3=-9$$

• Because taking a square root always adds a negative

Multiple Choice

$$x^{2\ }=\ 49$$

• x = 7 or x = -7

• x = 6 or x = -6

• x = 8 or x = -8

• x = 9 or x = -9

• x = $$\sqrt[]{25}$$

  or

  x = $$-\sqrt[]{25}$$

Multiple Choice

$$x^2\ =50$$

• x = 5 or x = -5

• x = 10 or x = -10

• x = 7or x = -7

• x = 6 or x = -6

• x = $$\sqrt[]{50}$$ or

  x = $$-\ \sqrt[]{50}$$

Multiple Choice

$$x^{2\ }=144$$

• x = 12 or x = -12

• x = 10 or x = -10

• x = 9 or x = -9

• x = 13 or x = -13

• $$x\ =\ \sqrt[]{72\ }$$

  or

  $$x\ =\ -\sqrt[]{72}$$

Multiple Choice

$$x^2+5\ =54$$

• x = 7 or x = -7
• x = 10 or x = -10
• x = 8 or x = -8
• x = 6 or x = -6
• x = 9 or x = -9

Multiple Choice

$$x^2+11=92$$

• ±6
• ±7
• ±9
• ±8
• ±10

Multiple Choice

$$14\ +x^2=39$$

• x = ±6
• x = ±4
• x = ±5
• x = ±3
• x = ±7

Multiple Choice

$$x^2+1=64$$

• x = ± $$\sqrt[]{62}$$

• x = ± $$\sqrt[]{63}$$

• x = ± $$\sqrt[]{65}$$

• x = ± $$\sqrt[]{64}$$

• x = ±√61

Multiple Choice

$$x^2-8=28$$

• x = ±12
• x = ±10
• x = ±2
• x = ±4
• x = ±6

Multiple Choice

$$x^2-\ 11=25$$

• x = ±15
• x = ±6
• x = ±10
• x = ±7
• x = ±5

Multiple Choice

$$-7\ +x^2=42$$

• ±√35
• ±√42
• ±√-7
• ±√49
• ±7

Multiple Choice

$$-10+x^2=16$$

• x = 13 or x = -13

• x = 6 or x = -6

• x = 4 or x = -4

• x = 5 or x = -5

• x = $$\sqrt[]{26}$$ and x = $$-\sqrt[]{26}$$

Multiple Choice

$$14-x^2=5$$

• x = ±3
• x = ±4
• x = ±6
• x = ±2
• x = ±5

Multiple Choice

$$9-x^2=8$$

• x = ±5
• x = ±4
• x = ±2
• x = ±1
• x = ±3

Multiple Choice

$$-6-x^2=10$$

• x = 4 or x = -4

• x = 2 or x = -2

• No solution
• x = 3 or x = -3

• x = 8 or x = -8

HOW IS THERE NO SOLUTION?!

Multiple Choice

$$5x^2=20$$

• x = 2

  OR

  x= -2

• x = 5

  OR

  x= -5

• x = 3

  OR

  x = -3

• x = 2

  AND

  x = -2

• x = 5

  AND
  x = -5

Multiple Choice

$$12x^2=192$$

• x = ±8
• x = 6

  AND

  x = -6

• x = 6

  OR

  x = -6

• x = 4

  AND

  x = -4

• x = 4

  OR

  x = -4

Multiple Choice

$$4x^2=80656$$

• x = 71

  OR

  x = -71

• x = 71

  OR

  x = -71

• x = 142

  AND

  x = -142

• x = ±284
• x = 142

  OR

  x = -142

Multiple Choice

What does the symbol $$\pm$$ mean?

• Positive

  OR

  Negative

• Positive

  AND

  Negative

• Plus

  AND

  Minus

• Approximately

• Add and then Divide

Multiple Choice

$$\frac{x^2}{4}=4$$

• x = ±4

• x = ±2

• x = ±3

• x = ±5

• x = -4

Multiple Choice

$$\frac{x^2}{7}=7$$

• ±14
• ±7
• ±49
• ±2
• ±1

Multiple Choice

$$4x^2+1=65$$

• x = ±6
• x = ±2
• x = ±8
• x = ±10
• x = ±4

Multiple Choice

$$\frac{x^2}{5}+5=10$$

• x = ±10

• x = ±25

• x = ±6

• x = ±5
• No Solution

Multiple Choice

$$2x^2-22=140$$

• x = 10 or x = -10
• x = 8 or x = -8
• x = 6 or x = -6
• x = 9 or x = -9
• x = 7 or x = -7

Multiple Choice

$$\frac{x^2-19}{3}=10$$

• ±12

• ±20

• ±7

• ±5

• ±15

Multiple Choice

A small house is composed of four identical square rooms and a room that's 65 square feet.

If the total square footage of the house is 321 square feet, how wide is a wall in the square rooms?

• 8 feet wide

• 10 feet wide

• 12 feet wide

• 6 feet wide

• 4 feet wide

"A small house is composed of four identical square rooms..."

​Explanation:

​"...and a room that is 65 square feet..."

" ...​If the total square footage of the house is 321 feet..."

​"...how wide are the walls in the square rooms?"

​...X = 8 feet

Multiple Choice

$$\frac{\left(7\cdot x^2+21\right)}{7}=147$$

• ±12

• ±11

• ±9

• ±8

• ±7

Multiple Choice

$$\frac{3\cdot x^2+7-3}{9-3}=64-12$$

• ±3

• ±6

• ±5

• ±4

• ±2