Answer:
- 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
Step-by-step 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.
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
x² + 7x + 12 = 0
a = 1
b = 7
c = 12
[tex]x=\frac{-7±\sqrt{7^{2} -4((1)(12))} }{2(1)}[/tex]
[tex]x=\frac{-7±\sqrt{49 -4((1)(12))} }{2(1)}[/tex]
[tex]x=\frac{-7±\sqrt{49 -48} }{2(1)}[/tex]
[tex]x=\frac{-7±\sqrt{1} }{2(1)}[/tex]
[tex]x=\frac{-7±1 }{2(1)}[/tex]
[tex]x=\frac{-7±1 }{2}[/tex]
Two separate equations
[tex]x=\frac{-7+1 }{2}[/tex]
x = - 6 ÷ 2
x = - 3
[tex]x=\frac{-7-1 }{2}[/tex]
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.
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
a = 1
b = - 2
c = 0
[tex]x=\frac{-(-2)±\sqrt{(-2)^{2} -4((1)(0))} }{2(1)}[/tex]
[tex]x=\frac{-(-2)±\sqrt{(-2)^{2} -4((1)(0))} }{2(1)}[/tex]
[tex]x=\frac{-(-2)±\sqrt{4 -4((1)(0))} }{2(1)}[/tex]
[tex]x=\frac{-(-2)±\sqrt{4 +0} }{2(1)}[/tex]
[tex]x=\frac{-(-2)±\sqrt{4} }{2(1)}[/tex]
[tex]x=\frac{2±2 }{2(1)}[/tex]
[tex]x=\frac{2±2 }{2}[/tex]
Two separate equations
[tex]x=\frac{2+2}{2}[/tex]
[tex]x=\frac{2-2}{2}[/tex]
x = 4 ÷ 2
x = 2
x = 0 ÷ 2
x = 0
