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Solving the Equation

by Kerk
(Melaka, Malaysia)











































(10q - 250)q = 2000 + 75q

solve the equation for variable "q"

Begin by using the distributive law to eliminate the parentheses on the left side of the equation

Comments for Solving the Equation

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Jun 18, 2011
Solving the Equation
by: Staff


The question:

by Kerk
(Melaka, Malaysia)

(10q - 250)q = 2000 + 75q


The answer:

(10q - 250)q = 2000 + 75q

Using the distributive law, eliminate the parentheses on the left side of the equation

10q*q - 250*q = 2000 + 75q

10q² - 250q = 2000 + 75q

Subtract 75q from each side of the equation

10q² - 250q - 75q = 2000 + 75q - 75q

10q² - 325q = 2000 + 75q - 75q

10q² - 325q = 2000 + 0

10q² - 325q = 2000


Subtract 2000 from each side of the equation

10q² - 325q - 2000 = 2000 - 2000

10q² - 325q - 2000 = 0


Simplify the equation by dividing each side of the equation by 5

(10q² - 325q - 2000)/5 = 0/5

(10q² - 325q - 2000)/5 = 0

10q²/5 - 325q/5 - 2000/5 = 0

(10/5)*q² - (325/5)*q - 2000/5 = 0

(2)*q² - (65)*q - 400 = 0

2q² - 65q - 400 = 0

-------------------------------

Use the quadratic equation to find the two solutions for q

aq² + bq + c = 0

q = [-b ± sqrt(b² - 4ac)]/2a

a = 2
b = -65
c = -400

-------------------------------

q = {-(-65) ± sqrt[(-65)² - 4*2*(-400)]}/(2*2)

q = {65 ± sqrt[4225 + 3200]}/(4)

q = {65 ± sqrt[7425]}/(4)

q = {65 ± 86.1684}/(4)


1st solution

q = {65 + 86.1684}/(4)

q = {151.168}/(4)

q = 37.7921


2nd solution

q = {65 - 86.1684}/(4)

q = {-21.1684}/(4)

q = -5.2921


The final answer to your problem is:

q = 37.7921
q = -5.2921


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Check the work. Substitute 37.7921 for q and -5.2921 for q in the original equation.


q = 37.7921


(10q - 250)q = 2000 + 75q


(10*37.7921 - 250)*37.7921 = 2000 + 75*37.7921


(377.921 - 250)* 37.7921 = 2000 + 75*37.7921

127.921*37.7921 = 2000 + 75*37.7921

4834.4 = 4834.4, OK




q = -5.2921


(10q - 250)q = 2000 + 75q


[10*(-5.2921) – 250]*(-5.2921) = 2000 + 75*(-5.2921)


(-52.921 - 250)*(-5.2921) = 2000 + 75*(-5.2921)

(-302.921)*(-5.2921) = 2000 + 75*(-5.2921)

1603.09 = 1603.09, OK



Thanks for writing.

Staff
www.solving-math-problems.com



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