Respuesta :

Substituting the {3,-11/3} the equation is satisfied for the both values individually. Also it can be satisfied by solving the equation 3x2+2x-33=0 and giving the roots as x=3 and x=-11/3

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Answer:  The solution set is [tex]\{3,-\dfrac{11}{3}\}.[/tex]

Step-by-step explanation:  We are given to determine the solution set of the following quadratic equation:

[tex](3x+1)^2-100=0.[/tex]

We will be using the factorization method and the following algebraic identity in the solution:

[tex](a+b)^2=a^2+2ab+b^2.[/tex]

The solution is as follows:

[tex](3x+1)^2-100=0\\\\\Rightarrow 9x^2+6x+1-100=0\\\\\Rightarrow 9x^2+6x-99=0\\\\\Rightarrow 3x^2+2x-33=0\\\\\Rightarrow 3x^2+11x-9x-33=0\\\\\Rightarrow x(3x+11)-3(3x+11)=0\\\\\Rightarrow (x-3)(3x+11)=0\\\\\Rightarrow x-3=0,~~3x+11=0\\\\\Rightarrow x=3,~~x=-\dfrac{11}{3}.[/tex]

Thus, the solution set is [tex]\{3,-\dfrac{11}{3}\}.[/tex]

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