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solve the two possible answers of (x-9)(x+5)=0

Sagot :

jacob193

Answer:

The two roots of this equation are [tex](-5)[/tex] and [tex]9[/tex].

Step-by-step explanation:

In this question, the goal is to find the values of [tex]x[/tex] that would satisfy this equation- in other words, the value of [tex]x[/tex] should set expression on the left side of the equation [tex](x - 9)\, (x + 5)[/tex] to [tex]0[/tex].

Observe that the expression [tex](x - 9)\, (x + 5)[/tex] is the product of two linear terms, [tex](x - 9)[/tex], and [tex](x + 5)[/tex]. The product of the two is [tex]0[/tex] as long as either of the two terms is [tex]0[/tex]. Hence, the values of [tex]x[/tex] that would satisfy the overall equation [tex](x - 9)\, (x + 5) = 0[/tex] would be the collection of values that would sete either of these terms to [tex]0[/tex].

For example, if [tex](x - 9)[/tex] is to be set to [tex]0[/tex]:

[tex]x - 9 = 0[/tex].

[tex]x = 9[/tex].

Likewise, if [tex](x + 5)[/tex] is to be set to [tex]0[/tex]:

[tex]x + 5 = 0[/tex].

[tex](x + 5) - 5 = 0 -5[/tex].

[tex]x = (-5)[/tex].

In other words, the values of [tex]x[/tex] that would satisfy this equation are [tex](-5)[/tex] and [tex]9[/tex].

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