Question

Which equation has the same solution as 2x^2+16x-10=0

Answer 1

D
Divide the whole thing by 2
2(X^2+8x-5)
X^2+8x. =5
Half of 8 is 4 sq it so you add 16
X^2+8x+16= 5+16
(X+4)^2=21

Answer 2

Answer:  The correct option is (D) $(x+4)^2=21.$

Step-by-step explanation:  We are given to select the correct equation that has the same solution as the following quadratic equation:

$2x^2+16x-10=0~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be trying to apply the method of completing the square to the given equation.

From equation (i), we have

$2x^2+16x-10=0\\\\\Rightarrow x^2+8x-5=0\\\\\Rightarrow x^2+2\times x\times 4+4^2-5=4^2\\\\\Rightarrow (x+4)^2=16+5\\\\\Rightarrow (x+4)^2=21.$

Thus, the required equation with the same solution as the given equation si $(x+4)^2=21.$

Option (D) is CORRECT.