# How do you solve the equation x^2+1.4x+0.49=0.81 by completing the square?

Dec 18, 2016

$x = 0.2 \text{ }$ or $\text{ } x = - 1.6$

#### Explanation:

We will use the difference of squares identity, which can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Given:

${x}^{2} + 1.4 x + 0.49 = 0.81$

Both the left hand and right hand side of this equation are perfect squares already:

$\left(x + {0.7}^{2}\right) = {x}^{2} + 1.4 x + 0.49 = 0.81 = {0.9}^{2}$

Hence:

$0 = \left(x + {0.7}^{2}\right) - {0.9}^{2}$

$\textcolor{w h i t e}{0} = \left(\left(x + 0.7\right) - 0.9\right) \left(\left(x + 0.7\right) + 0.9\right)$

$\textcolor{w h i t e}{0} = \left(x - 0.2\right) \left(x + 1.6\right)$

Hence:

$x = 0.2 \text{ }$ or $\text{ } x = - 1.6$