# How do you solve 3x^2+5=5x^2+10?

Feb 10, 2017

$x = + i \sqrt{\frac{5}{2}}$ and $x = - i \sqrt{\frac{5}{2}}$

#### Explanation:

Although this is under the section "completing the square," that is not what is required to solve this problem.

Step 1. Move everything to the left hand side

$3 {x}^{2} - 5 {x}^{2} + 5 - 10 = 0$

Step 2. Combine like terms

$- 2 {x}^{2} - 5 = 0$

Step 3. Solve for $x$

$- 2 {x}^{2} - 5 = 0$
$- 2 {x}^{2} = 5$
${x}^{2} = - \frac{5}{2}$
$x = \pm i \sqrt{\frac{5}{2}}$