Answer :
Answer: The correct option is (D) x = -6, x = 4.
Step-by-step explanation: We are given to complete the square to solve the following quadratic equation :
[tex]x^2+2x-14=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following square formula :
[tex]a^2+2ab+b^2=(a+b)^2.[/tex]
From equation (i), we have
[tex]x^2+2x-14=10\\\\\Rightarrow x^2+2x=10+14\\\\\Rightarrow x^2+2\times x\times1+1^2=24+1^2\\\\\Rightarrow (x+1)^2=24+1\\\\\Rightarrow (x+1)^2=25\\\\\Rightarrow x+1=\pm\sqrt{25}~~~~~~~~~~~~~~~~~~~~~~~~~~~~`[\textup{taking square root on both sides}]\\\\\Rightarrow x+1=\pm5\\\\\Rightarrow x=-1\pm5\\\\\Rightarrow x=-1+5,~-1-5\\\\\Rightarrow x=4,~-6.[/tex]
Thus, the required solution of the given equation is x = -6 and x = 4.
Option (D) is CORRECT.