What is the value of variable x  (x+3)^2-2(9x-13)=0 ?

Expert Answers
justaguide eNotes educator| Certified Educator

The equation to be solved is : (x+3)^2-2(9x-13)=0

(x+3)^2 - 2(9x - 13) = 0

=> x^2 + 9 + 6x -18x + 26 = 0

=> x^2 - 12x + 35 = 0

=> x^2 - 7x - 5x + 35 = 0

=> x(x - 7) - 5(x - 7) = 0

=> (x - 5)(x - 7) = 0

x = 5 and x = 7

The solution of the equation is x = 5 and x = 7.

giorgiana1976 | Student

To determine the values of x, we'll have to solve the quadratic equation.

For this reason, we'll expand the square and we'll remove the brackets.

We'll expand the square using the formula:

(a+b)^2 = a^2 + 2ab + b^2

Now, we'll expand (x+3)^2:

(x+3)^2 = x^2 + 6x + 9

The equation will become:

x^2 + 6x + 9 - 18x + 26 = 0

We'll combine like terms:

x^2 - 12x + 35 = 0

We'll apply quadratic formula;

x1 = [12+sqrt(144 - 140)]/2

x1 = (12+2)/2

x1 = 7

x2 = (12-2)/2

x2 = 5

The solutions of the equation are {5 ; 7}.