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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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}.

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