Question

Solve x^2 − 4x = 14.

Answer 1

minus 14 from both sides
x²-4x-14=0
use quadratic formula because we cant factor

for
ax²+bx+c=0

`x= (-b+/- √(b^2-4ac) )/(2a)`

so
1x²-4x-14=0
a=1
b=-4
c=-14


`x= (-(-4)+/- √((-4)^2-4(1)(-14)) )/(2(1))`

`x= (4+/- √(16+56) )/(2)`

`x= (4+/- √(72) )/(2)`

`x= (4+/- 6√(2) )/(2)`

`x= 2+/- 3√(2)`

the solutions are
x=2+√3 and
x=2-√3