# How do you solve 4x^2=25?

Apr 17, 2016

$x = \pm \frac{5}{2}$

#### Explanation:

Use the color(gold)("golden rule" of Algebra

$\text{What we do on one side,must be done on the other side also}$

Our aim is to isolate $x$ to find its value

color(blue)(4x^2=25

Divide both sides by $4$

$\rightarrow \frac{\cancel{4} {x}^{2}}{\cancel{4}} = \frac{25}{4}$

$\rightarrow {x}^{2} = \frac{25}{4}$

Take the square root of both sides

rarrsqrt(x^2)=sqrt(25/4

$\rightarrow x = \sqrt{\frac{25}{4}}$

Remember that,if we take the square root of a number,it can be positive or negative

So,

$\rightarrow x = \pm \sqrt{\frac{25}{4}}$

Use the property

color(brown)(sqrt(x/y)=sqrtx/sqrty

$\rightarrow x = \pm \frac{\sqrt{25}}{\sqrt{4}}$

color(blue)(rArrx=+-5/2

Remember that the symbol $\pm$ means Plus or Minus

it indicates that

rArrcolor(blue)(x=5/2,-5/2