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Algebra Level 1

What are the solutions to the equation

x 2 = 4 ? x^2 = 4 ?

x = 1 , 1 x = 1, -1 x = 2 , 2 x = 2, -2 x = 2 x=-2 x = 0 x=0

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8 solutions

x 2 = 4 x^2=4

Extract the square root of both sides.

x 2 = ± 4 \sqrt{x^2}=\pm \sqrt4

x = ± 2 x=\pm 2

Therefore, x = 2 x=2 and x = 2 x=-2

Check:

when x = 2 x=2 , we have

2 2 = 4 2^2=4

4 = 4 4=4 (true)

when x = 2 x=-2

( 2 ) 2 = 4 (-2)^2=4

4 = 4 4=4 (true)

Therefore, the solutions are

x = 2 x=2 and x = 2 x=-2 .

What about ± 2 i \pm 2i ?

. . - 2 weeks, 2 days ago
Calvin Lin Staff
Jun 26, 2014

The solutions are x = 2 , 2 x = 2, -2 .

We can factorize the equation as 0 = x 2 4 = ( x 2 ) ( x + 2 ) 0 = x^2 - 4 = (x-2)(x+2) , hence the solutions are x = 2 , 2 x = 2, -2 .

I suckered at math. I'm never gonna be good at it (v_v)

Cici Duggins - 6 years, 10 months ago

algebraaaaaaaaaaaa.....

PUSHPESH KUMAR - 6 years, 11 months ago

it was so simple (-2,2) is the answer

Amit Chauhan - 6 years, 10 months ago

Owhhh ..I forgot that 2 in x=2 has no square......LOL

kelvin gonzales - 6 years, 11 months ago
Jaay Thakur
Jul 5, 2014

The solutions are x=2,-2 We can substitute X by 2 and -2 in the given equation. Hence the solutions are x=2,-2.

Great.. nice solution...

Heder Oliveira Dias - 6 years, 11 months ago
. .
May 8, 2021

x 2 = 4 x = ± 2 x ^ { 2 } = 4 \Leftrightarrow x = \pm 2 by taking square root to each sides.

Gia Hoàng Phạm
Sep 22, 2018

x 2 = 4 x = ± 2 x^2=4 \implies x=\pm 2

x 2 = 4 \large x^2 = 4 , then

x = 2 , 2 \large x = 2, -2

Betty BellaItalia
Apr 22, 2017

Prince Mishra
Jul 8, 2014

root of square of gives ans in +ve and -ve both

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