Determine the solution set of (3x + 1)2 - 100 = 0.
{3, -3}
{3, -11/3}
{-11/3, -3}
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 \(\{3,-\dfrac{11}{3}\}.\)
Step-by-step explanation: We are given to determine the solution set of the following quadratic equation:
\((3x+1)^2-100=0.\)
We will be using the factorization method and the following algebraic identity in the solution:
\((a+b)^2=a^2+2ab+b^2.\)
The solution is as follows:
\((3x+1)^2-100=0\\\\\Rightarrow 9x^2+6x+1-100=0\\\\\Rightarrow 9x^2+6x-99=0\\\\\Rightarrow 3x^2+2x-33=0\\\\\Rightarrow 3x^2+11x-9x-33=0\\\\\Rightarrow x(3x+11)-3(3x+11)=0\\\\\Rightarrow (x-3)(3x+11)=0\\\\\Rightarrow x-3=0,~~3x+11=0\\\\\Rightarrow x=3,~~x=-\dfrac{11}{3}.\)
Thus, the solution set is \(\{3,-\dfrac{11}{3}\}.\)