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Question
x^{2}\times 36x-462
Simplify the expression
36x^{3}-462
Evaluate
x^{2}\times 36x-462
Solution
More Steps
Evaluate
x^{2}\times 36x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 36
Add the numbers
x^{3}\times 36
Use the commutative property to reorder the terms
36x^{3}
36x^{3}-462
Show Solutions
Factor the expression
6\left(6x^{3}-77\right)
Evaluate
x^{2}\times 36x-462
Multiply
More Steps
Evaluate
x^{2}\times 36x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 36
Add the numbers
x^{3}\times 36
Use the commutative property to reorder the terms
36x^{3}
36x^{3}-462
Solution
6\left(6x^{3}-77\right)
Show Solutions
Find the roots
x=\frac{\sqrt[3]{2772}}{6}
Alternative Form
x\approx 2.341243
Evaluate
x^{2}\times 36x-462
To find the roots of the expression,set the expression equal to 0
x^{2}\times 36x-462=0
Multiply
More Steps
Multiply the terms
x^{2}\times 36x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 36
Add the numbers
x^{3}\times 36
Use the commutative property to reorder the terms
36x^{3}
36x^{3}-462=0
Move the constant to the right-hand side and change its sign
36x^{3}=0+462
Removing 0 doesn't change the value,so remove it from the expression
36x^{3}=462
Divide both sides
\frac{36x^{3}}{36}=\frac{462}{36}
Divide the numbers
x^{3}=\frac{462}{36}
\text{Cancel out the common factor }6
x^{3}=\frac{77}{6}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{x^{3}}=\sqrt[3]{\frac{77}{6}}
Calculate
x=\sqrt[3]{\frac{77}{6}}
Solution
More Steps
Evaluate
\sqrt[3]{\frac{77}{6}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{77}}{\sqrt[3]{6}}
Multiply by the Conjugate
\frac{\sqrt[3]{77}\times \sqrt[3]{6^{2}}}{\sqrt[3]{6}\times \sqrt[3]{6^{2}}}
Simplify
\frac{\sqrt[3]{77}\times \sqrt[3]{36}}{\sqrt[3]{6}\times \sqrt[3]{6^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{77}\times \sqrt[3]{36}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{77\times 36}
Calculate the product
\sqrt[3]{2772}
\frac{\sqrt[3]{2772}}{\sqrt[3]{6}\times \sqrt[3]{6^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{6}\times \sqrt[3]{6^{2}}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{6\times 6^{2}}
Calculate the product
\sqrt[3]{6^{3}}
\text{Reduce the index of the radical and exponent with }3
6
\frac{\sqrt[3]{2772}}{6}
x=\frac{\sqrt[3]{2772}}{6}
Alternative Form
x\approx 2.341243
Show Solutions
