Jackg7955
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Complete the square to transform the quadratic equation into the form
(x – p)^2 = q. x^2 - 8x - 10 = 18
A) (x - 8)^2 = 14
B) (x - 4)^2 = 44
C) (x - 8)^2 = -14
D) (x - 4)2 = -44

Respuesta :

The square of a binomial is written like

[tex](x\pm a)^2 = x^2\pm 2ax + a^2[/tex]

In your case, you have [tex]2ax=-8x[/tex], which implies [tex]a=-4[/tex]

So, we want to write

[tex](x-4)^2 = x^2-8x+16[/tex]

But our left hand side is

[tex]x^2-8x-10[/tex]

If we add 26 to both sides, we have

[tex] x^2 - 8x - 10 +26 = 18+26 \iff x^2-8x+16=44 \iff (x-4)^2=44[/tex]

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