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Marina solved the quadratic equation 9x^2 - 36x - 720 = 0 by completing the square. In the process, she came up with the equivalent equation

(x + r)^2 = s

where r and s are constants. What is s?

 Nov 26, 2020
 #1
avatar+419 
0

Divide by 9 on both sides

 

x^2 + 6x - 80 = 0

 

So x^2 + 6x = 80

 

(6/2)^2 = 9

 

s = 80 + 9 = 89

 Nov 26, 2020
 #2
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0

Solve for x:
9 x^2 - 36 x - 720 = 0

Divide both sides by 9:
x^2 - 4 x - 80 = 0

Add 80 to both sides:
x^2 - 4 x = 80

Add 4 to both sides:
x^2 - 4 x + 4 = 84

Write the left hand side as a square:
(x - 2)^2 = 84

Take the square root of both sides:
x - 2 = 2 sqrt(21) or x - 2 = -2 sqrt(21)

Add 2 to both sides:
x = 2 + 2 sqrt(21) or x - 2 = -2 sqrt(21)

Add 2 to both sides:


x = 2 + 2 sqrt(21)      or      x = 2 - 2 sqrt(21)

 

[ (2+2sqrt(21))  +  (2 - 2sqrt(21))]^2 ==4^2 ==16

 Nov 27, 2020
 #3
avatar+116126 
+1

Factor out the 9

 

9 (x^2  - 4x - 80)  = 0

 

Take 1/2  of 4 = 2...square it  = 4.....add and subtract it  within the parentheses

 

9 ( x^2 - 4x  + 4  -  80  - 4)     factor the first three terms  ....simplify the  rest

 

9 [ ( x - 2)^2  - 84  ]  =  0       divide both sides  by  9

 

(x - 2)^2  - 84  = 0

 

(x - 2)^2  =  84

 

r = - 2     s  = 84

 

cool cool cool

 Nov 27, 2020
edited by CPhill  Nov 27, 2020

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