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Which quadratic equation is equivalent to [tex]$(x+2)^2+5(x+2)-6=0$[/tex]?

A. [tex]$(u+2)^2+5(u+2)-6=0$[/tex] where [tex][tex]$u=(x-2)$[/tex][/tex]

B. [tex]$u^2+4+5u-6=0$[/tex] where [tex]$u=(x-2)$[/tex]

C. [tex][tex]$u^2+5u-6=0$[/tex][/tex] where [tex]$u=(x+2)$[/tex]

D. [tex]$u^2+u-6=0$[/tex] where [tex][tex]$u=(x+2)$[/tex][/tex]


Sagot :

To determine the quadratic equation equivalent to [tex]\((x+2)^2 + 5(x+2) - 6 = 0\)[/tex], we will make a substitution.

Let's set [tex]\(u = x + 2\)[/tex]. Then, the original equation can be rewritten in terms of [tex]\(u\)[/tex]:

1. Start with the original equation:
[tex]\[ (x+2)^2 + 5(x+2) - 6 = 0 \][/tex]
With [tex]\(u = x + 2\)[/tex], we substitute in place of [tex]\((x + 2)\)[/tex]:

[tex]\[ (u)^2 + 5(u) - 6 = 0 \][/tex]

2. Simplify this equation:

[tex]\[ u^2 + 5u - 6 = 0 \][/tex]

So, the quadratic equation equivalent to [tex]\((x+2)^2 + 5(x+2) - 6 = 0\)[/tex] is:
[tex]\[ u^2 + 5u - 6 = 0 \][/tex]
where [tex]\(u = x + 2\)[/tex].

Therefore, the correct answer is:
[tex]\[ u^2 + 5u - 6 = 0 \quad \text{where } u = (x+2) \][/tex]