+379 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 :)
+9466 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
+9466 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
