NeitoK
contestada

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

A: (x+4)^2=-3
B: (x+4)^2=-11
C: (x+4)^2=13
D: (x+4)^2=21

Respuesta :

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:  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.