Question

Solve By using square roots
solve by factoring

Answer 1

- 5m² = - 125

m = 5 and m = - 5

4n² - 64 = 0

n = 4 and n = - 4

x² + 7x + 12 = 0

x = - 3 and x = - 4

5x² - 10x = 0

x = 2 and x = 0

Explanation:

- 5m² = - 125

- 5m² × - 1 = - 125 × - 1

5m² = 125

5m² ÷ 5 = 125 ÷ 5

m² = 25

√m² = √25

m = 5

m = - 5

4n² - 64 = 0

4n² - 64 + 64 = 0 + 64

4n² = 64

4n² ÷ 4 = 64 ÷ 4

n² = 16

√n² = √16

n = 4

n = - 4

x² + 7x + 12 = 0

(x + 3)(x + 4) = 0

x + 3 = 0

x + 4 = 0

x + 3 = 0

x + 3 - 3 = 0 - 3

x = - 4

x + 4 = 0

x + 4 - 4 = 0 - 4

x = - 4

5x² - 10x = 0

5(x² - 2x) = 0

5(x - 2) · x = 0

x - 2 = 0

x = 0

x - 2 = 0

x - 2 + 2 = 0 + 2

x = 2

x = 0

Quadratic Formula

Ignore the A before the ±. It wouldn't let me type it correctly.

`x=\frac{-b±\sqrt{b^(2) -4ac} }{2a}`

x² + 7x + 12 = 0

a = 1

b = 7

c = 12

`x=\frac{-7±\sqrt{7^(2) -4((1)(12))} }{2(1)}`

`x=(-7±√(49 -4((1)(12))) )/(2(1))`

`x=(-7±√(49 -48) )/(2(1))`

`x=(-7±√(1) )/(2(1))`

`x=(-7±1 )/(2(1))`

`x=(-7±1 )/(2)`

Two separate equations

`x=(-7+1 )/(2)`

x = - 6 ÷ 2

x = - 3

`x=(-7-1 )/(2)`

x = - 8 ÷ 2

x = - 4

5x² - 10x = 0

5(x² - 2x) = 0

(5(x² - 2x)) ÷ 5 = 0 ÷ 5

x² - 2x = 0

Ignore the A before the ±. It wouldn't let me type it correctly.

`x=\frac{-b±\sqrt{b^(2) -4ac} }{2a}`

a = 1

b = - 2

c = 0

`x=\frac{-(-2)±\sqrt{(-2)^(2) -4((1)(0))} }{2(1)}`

`x=\frac{-(-2)±\sqrt{(-2)^(2) -4((1)(0))} }{2(1)}`

`x=(-(-2)±√(4 -4((1)(0))) )/(2(1))`

`x=(-(-2)±√(4 +0) )/(2(1))`

`x=(-(-2)±√(4) )/(2(1))`

`x=(2±2 )/(2(1))`

`x=(2±2 )/(2)`

Two separate equations

`x=(2+2)/(2)`

`x=(2-2)/(2)`

x = 4 ÷ 2

x = 2

x = 0 ÷ 2

x = 0

Answer 2

1.
times -1 both sides
5m^2=125
divide both sides by 5
m^2=25
sqrt both sides
m=-5 and 5


2.
4m^2-64=0
add 64
4m^2=64
divide 4
m^2=16
sqrt
m=-4 and 4

3.
what 2 numbers multiply to 12 and add to 7?
3 and 4
(x+3)(x+4)=0
set to zero
x+3=0
x=-3

x+4=0
x=-4

x=-4 and -3



4. factor out 5x
5x(x-2)=0
set to zero
5x=0
x=0

x-2=0
x=2

x=0 and 2