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Patricia is trying to solve the following equation by completing the square: 25x^2+20x-10 = 0. She successfully rewrites the above equation in the following form: (ax+b)^2 = c, where a,b  and c are integers and a>0. What is the value of a+b+c?

Thank you :)

Jun 8, 2019

#1
+3

25x2 + 20x - 10  =  0

Rewrite the equation as...

(5x)2 + 4(5x) - 10  =  0

To make it clearer, let  u  =  5x   and then substitute  u  in for  5x

u2 + 4u - 10  =  0

Add  10  to both sides of the equation.

u2 + 4u  =  10

Add  4  to both sides of the equation to complete the square on the left side.

u2 + 4u + 4  =  14

Factor the perfect square trinomial on the left side.

(u + 2)2  =  14

And since  u  =  5x  we can substitute  5x  in for  u

(5x + 2)2  =  14

Now the equation is in the form  (ax + b)2  =  c   where  a,  b,  and  c  are integers and  a > 0 .

a + b + c  =  5 + 2 + 14  =  21

Jun 8, 2019

#1
+3

25x2 + 20x - 10  =  0

Rewrite the equation as...

(5x)2 + 4(5x) - 10  =  0

To make it clearer, let  u  =  5x   and then substitute  u  in for  5x

u2 + 4u - 10  =  0

Add  10  to both sides of the equation.

u2 + 4u  =  10

Add  4  to both sides of the equation to complete the square on the left side.

u2 + 4u + 4  =  14

Factor the perfect square trinomial on the left side.

(u + 2)2  =  14

And since  u  =  5x  we can substitute  5x  in for  u

(5x + 2)2  =  14

Now the equation is in the form  (ax + b)2  =  c   where  a,  b,  and  c  are integers and  a > 0 .

a + b + c  =  5 + 2 + 14  =  21

hectictar Jun 8, 2019