3 years ago

What is the radical expression

Mathematics

1 answer:

Margaret [11]3 years ago

6 0

$5x^{\frac{1}{4} }=5\cdot x^{\frac{1}{4}}= 5\sqrt[4]{x} \\\\because\\\\a^{\frac{1}{n} }=\sqrt[n]{a}$

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Solve 5x(x-6)(4x+9)=0

xxTIMURxx [149]

Greetings and Happy Holidays!

Solve for x.
$5x(x-6)(4x+9)=0$ <span>

Distribute the parenthesis:
</span> $5x(x-6)(4x+9)=0$

$(5x^2-30x)(4x+9)=0$

$(20x^3-120x^2)+(45x^2-270x)=0$

Combine like terms:
$20x^3-75x^2-270x=0$

Factor out GCF (5x):
$5x(4x^2-15x-54)=0$

Factor the Complex Trinomial:
$5x(4x^2+9x-24x-54)=0$

$5x(x(4x+9)-6(4x-9))=0$

$5x((4x+9)(x-6))=0$

Set Factors to Equal 0:
$5x=0$

$x=0$

or

$4x+9=0$

$4x=-9$

$x=\frac{-9}{4}$

or

$x-6=0$

$x=6$

The Answers Are:
$\boxed{x=0} \\ \boxed{x= \frac{-9}{4}} \\ \boxed{x=6}$

I hope this helped!
-Benjamin

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