SOLUTION: Solve by using the quadratic formula... 1. 2x^2-7x=5 Solve... 1. x^2+10x+16=0 The demand and supply equations for a certain item are given by D=-5p+40/S=-p^2+30p-8..Find th

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve by using the quadratic formula... 1. 2x^2-7x=5 Solve... 1. x^2+10x+16=0 The demand and supply equations for a certain item are given by D=-5p+40/S=-p^2+30p-8..Find th      Log On


   

Question 86408: Solve by using the quadratic formula...
1. 2x^2-7x=5
Solve...
1. x^2+10x+16=0
The demand and supply equations for a certain item are given by D=-5p+40/S=-p^2+30p-8..Find the equilibirum price...
Find the axis of symmetry...
1. y=x^2-7x+2

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by using the quadratic formula...
1. 2x^2-7x=5
2x^2 - 7x - 5 = 0; a=2; b=-7; c=-5
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-7%29+%2B-+sqrt%28+-7%5E2+-+4+%2A+2+%2A+-5+%29%29%2F%282%2A2%29+
x+=+%28%2B7+%2B-+sqrt%28+49+-+%28-40+%29%29%29%2F%284%29+
x+=+%28%2B7+%2B-+sqrt%28+89%29%29%2F%284%29+
Solution 1
x+=+%287+%2B+9.43398%29%2F4
x+=+16.43398%2F4
x = +4.1085
:
Solution 2
x+=+%287+-+9.43398%29%2F4
x+=+-2.43398%2F4
x = -.6085
:
:
Solve...
1. x^2+10x+16=0
Easily factored:
(x+8)(x+2) = 0
x = -8
x = -2
:
:
The demand and supply equations for a certain item are given by
D=-5p + 40 and S = -p^2 + 30p - 8.. Find the equilibrium price...
:
Equilibrium price occurs when D = S; therefore:
-5p + 40 = -p^2 + 30p - 8
:
p^2 - 5p - 30p + 40 + 8 = 0; arrange an equation on the left:
p^2 - 35p + 48 = 0
Solve this using the quadratic formula: a=1; b=-35; c=48 like we did above
You will find two values. It's lower value we want. p = $1.43
:
:
Find the axis of symmetry...
1. y=x^2-7x+2
:
The axis of symmetry formula: x = -b/(2a)
In this equation; a = 1; b = -7
x = -(-7)/(2*1)
x = +7/2
x = +3.5 is the axis of symmetry