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What substitution should be used to rewrite [tex][tex]$6(x+5)^2+5(x+5)-4=0$[/tex][/tex] as a quadratic equation?

A. [tex]u = (x+5)[/tex]
B. [tex]u = (x-5)[/tex]
C. [tex]u = (x+5)^2[/tex]
D. [tex]u = (x-5)^2[/tex]

Sagot :

GinnyAnswer
To rewrite the given equation [tex]\(6(x+5)^2 + 5(x+5) - 4 = 0\)[/tex] as a quadratic equation, we can use a substitution. The goal of the substitution is to simplify the expression into a standard quadratic form.

Let's examine the given equation:

[tex]\[ 6(x+5)^2 + 5(x+5) - 4 = 0 \][/tex]

We notice that the expression [tex]\(x+5\)[/tex] appears in both the quadratic term and the linear term. To simplify this, we can introduce a new variable [tex]\(u\)[/tex]. We set:

[tex]\[ u = (x+5) \][/tex]

With this substitution, the equation becomes:

[tex]\[ 6u^2 + 5u - 4 = 0 \][/tex]

Now, we have rewritten the original equation in the standard quadratic form using the substitution [tex]\(u = (x+5)\)[/tex].

So, the correct substitution to rewrite the original equation as a quadratic equation is:
[tex]\[ u = (x+5) \][/tex]

Therefore, the correct choice is:
[tex]\[ u = (x+5) \][/tex]
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