Answer: The correct option is (D) [tex](x+4)^2=21.[/tex]
Step-by-step explanation: We are given to select the correct equation that has the same solution as the following quadratic equation:
[tex]2x^2+16x-10=0~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be trying to apply the method of completing the square to the given equation.
From equation (i), we have
[tex]2x^2+16x-10=0\\\\\Rightarrow x^2+8x-5=0\\\\\Rightarrow x^2+2\times x\times 4+4^2-5=4^2\\\\\Rightarrow (x+4)^2=16+5\\\\\Rightarrow (x+4)^2=21.[/tex]
Thus, the required equation with the same solution as the given equation si [tex](x+4)^2=21.[/tex]
Option (D) is CORRECT.
