5a^2-13a+13=7

Question

It is solving and graphing problem.

Answer 1

5a^2-13a+13 = 7

Subtract 7 from each side.

5a^2-13a+13-7 = 7-7

5a^2-13a+6 = 0

5a^2-10a-3a+6 = 0

5a(a-2)-3(a-2) = 0

(a-2)(5a-3) = 0

a-2 = 0

Add 2 to each side.

a-2+2 = 0+2

a = 2

and 5a-3 = 0

Add 3 to each side.

5a-3+3 = 0+3

5a = 3

Divide to each side by 5.

5a/5 = 3/5

a = 3/5 = 0.6

Solution a = 2 and 0.6.

Graph

Comments

The quadratic equation is 5a^2 - 13a + 6 = 0.

The solutions of the quadratic equation are a = 0.6 and a = 2.

Graph the solution on the number line :

Note : A dot means that the points (0.6 and 2) are the solutions of the given equation.