# How do you solve 49x^2+3=21?

Oct 5, 2016

$= \frac{\pm 3 \sqrt{2}}{7}$

#### Explanation:

The first thing to notice is that this is a quadratic equation because it has ${x}^{2}$

To solve a quadratic, equation, we would usually make make it equal to 0.

However in this case, there is no $x$ term so we can use the method of finding a square root.

$49 {x}^{2} + 3 = 21$

$49 {x}^{2} = 18$

${x}^{2} = \frac{18}{49} \text{ "larr " isolate } {x}^{2}$

$x = \pm \sqrt{\frac{18}{49}} \text{ } \leftarrow$ there are 2 square roots to consider

$= \pm \sqrt{\frac{2 \times 3 \times 3}{7} ^ 2} \text{ } \leftarrow$ find prime factors of 18

$= \frac{\pm 3 \sqrt{2}}{7}$