Solve the equation with radicals $\sqrt[3]{x+5}=2\sqrt[3]{2x+6}$

Step-by-step Solution

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Final answer to the problem

$x=\frac{43}{-15}$
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Step-by-step Solution

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  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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1

Removing the variable's exponent raising both sides of the equation to the power of $3$

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$x+5=\left(2\sqrt[3]{2x+6}\right)^3$

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Unlock the first 3 steps of this solution

Learn how to solve equations problems step by step online. Solve the equation with radicals (x+5)^(1/3)=2(2x+6)^(1/3). Removing the variable's exponent raising both sides of the equation to the power of 3. The power of a product is equal to the product of it's factors raised to the same power. Solve the product 8\left(2x+6\right). Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side.

Final answer to the problem

$x=\frac{43}{-15}$

Exact Numeric Answer

$x=-2.8666667$

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Function Plot

Plotting: $\sqrt[3]{x+5}-2\sqrt[3]{2x+6}$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.

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