Question

Please show me how to solve for Xsquared - 21.75X = -15.75. I have the solution but do not know how to solve it.

Answer 1

$x^2-21.75x=-15.75 \\ x^2-21.75x+15.75=0$

Use the quadratic formula:
$x^2-21.75x+15.75=0 \\ \\ a=1 \\ b=-21.75 \\ c=15.75 \\ b^2-4ac=(-21.75)^2-4 \times 1 \times 15.75=473.0625-63=410.0625 \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-21.75) \pm \sqrt{410.0625}}{2 \times 1}=\frac{21.75 \pm 20.25}{2} \\ x=\frac{21.75-20.25}{2} \ \lor \ x=\frac{21.75+20.25}{2} \\ x=\frac{1.5}{2} \ \lor \ x=\frac{42}{2} \\ x=\frac{15}{20} \ \lor \ x=21 \\ x=\frac{3}{4} \ \lor \ x=21 \\ \boxed{x=\frac{3}{4} \hbox{ or } x=21}$