# How do you solve the equation x^2-4.7x=-2.8 by completing the square?

Jun 26, 2018

Shown below

#### Explanation:

${x}^{2} - 4.7 x = - 2.8$

Take the coefficient of the $x$ i.e. $- 4.7$ half it, then square it, and add to both sides

${x}^{2} - 4.7 x + {\left(\frac{4.7}{2}\right)}^{2} = - 2.8 + {\left(\frac{4.7}{2}\right)}^{2}$

${x}^{2} - 4.7 x + 5.5225 = 2.7225$

Then left hand side is a square polynomial:

${\left(x - 2.35\right)}^{2} = 2.7225$

Now sqrt both sides:

$x - 2.35 = \pm \sqrt{2.7225}$

$x = 2.35 \pm 1.65$

$x = \left\{0.7 , 4\right\}$