Question 799255
Check whether = (0.91 - sqrt(48.2981))/4.7 and = (0.91 + sqrt(48.2981))/4.7 are solutions to the equation -7.51p^2-7.03p-6.63=-7.94p-5.16p^2-11.68. 
:
-7.51p^2 - 7.03p - 6.63 = -7.94p - 5.16p^2 - 11.68. 
Combine like terms on the right
0 = = -7.94p + 7.03p - 5.16p^2 + 7.51p^2 - 11.68 + 6.63
0 =  -.91p + 2.35p^2 - 5.05
Arrange as a quadratic equation
2.35p^2 - .91p - 5.05 = 0 
Find the solutions using the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
where x=p; a=2.35; b=-.91; c=-5.05
{{{p = (-(-.91) +- sqrt(-.91^2-4*2.35*-5.05 ))/(2*2.35) }}}
:
{{{p = (.91 +- sqrt(.8281-(-47.47 )))/(4.7) }}}
Minus a minus is a plus
{{{p = (.91 +- sqrt(.8281+47.47))/(4.7) }}}
:
{{{p = (.91 + sqrt(48.2981))/4.7 }}}
and
{{{p = (.91 - sqrt(48.2981))/4.7 }}}
:
We proved that, indeed, these are the solutions to the given equation
:
Did this makes sense to you now? CK