Question

Complete the Square: 5x^2+16x-40=8 (please show your steps)

Answer 1

Answer:

Step-by-step explanation:

divide through by the coefficient of $x^{2}$

$\frac{5x^{2} }{5}$ + $\frac{16x}{5} + \frac{-40}{5} = \frac{8}{5}$

$x^{2} +\frac{16}{5}x -8 =\frac{8}{5}$

$x^{2} +\frac{16}{5} x = \frac{8}{5} +8$

$x^{2} + \frac{16}{5} x =\frac{48}{5}$

Add half of the square of the coefficient of x  to both sides $(\frac{1}{2} X \frac{16}{5} ) ^{2}$

$x^{2} + \frac{16}{5}x + (\frac{1}{2} X \frac{16}{5} )^{2} =$ $\frac{48}{5} +(\frac{1}{2} X \frac{16}{5} )^{2}$

$x^{2} +\frac{16}{5} x +(\frac{16}{10}) ^{2} =\frac{48}{5} +\frac{64}{25}$

$(x +\frac{16}{10})^{2} =\frac{304}{25}$

$x +\frac{16}{10} =$±$\sqrt{\frac{304}{25} }$

$x = -\frac{16}{10}$ ± $\sqrt{\frac{304}{25} }$

$x=-\frac{16}{10} + \sqrt{\frac{304}{25} }$ or$-\frac{16}{10} - \sqrt{\frac{304}{25} }$

$x = 1.89$ or -5.09