Question 232014
Use the quadratic formula to determine the exacty solutions of each quadratic equation. Then approximate each solution to the nearest hundredth.
y^2 - 5 = 0
y^2 = 5
y = +/-{{{sqrt(5)}}}
That is:
y ~ +/- 2.24
:
5w^2 = 2w + 1
5w^2 - 2w - 1 = 0
The quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this problem x - w; a=5; b=-2; c=-1
{{{w = (-(-2) +- sqrt(-2^2 - 4*5*-1 ))/(2*5) }}}
:
{{{w = (2 +- sqrt(4 - (-20) ))/10 }}}
:
{{{w = (2 +- sqrt(4 + 20 ))/10 }}}
;
{{{w = (2 +- sqrt(24 ))/10 }}}
Two solutions
{{{w = (2 +4.89898)/10}}}
w = {{{6.89898/10}}}
w ~ .69
And
{{{w = (2 - 4.89898)/10}}}
w = {{{-2.89898/10}}}
w ~ -.29