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Question
14x^{2}\times 33x-45=0
Solve the equation
x=\frac{\sqrt[3]{355740}}{154}
Alternative Form
x\approx 0.460105
Evaluate
14x^{2}\times 33x-45=0
Multiply
More Steps
Evaluate
14x^{2}\times 33x
Multiply the terms
462x^{2}\times x
Multiply the terms with the same base by adding their exponents
462x^{2+1}
Add the numbers
462x^{3}
462x^{3}-45=0
Move the constant to the right-hand side and change its sign
462x^{3}=0+45
Removing 0 doesn't change the value,so remove it from the expression
462x^{3}=45
Divide both sides
\frac{462x^{3}}{462}=\frac{45}{462}
Divide the numbers
x^{3}=\frac{45}{462}
\text{Cancel out the common factor }3
x^{3}=\frac{15}{154}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{x^{3}}=\sqrt[3]{\frac{15}{154}}
Calculate
x=\sqrt[3]{\frac{15}{154}}
Solution
More Steps
Evaluate
\sqrt[3]{\frac{15}{154}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{15}}{\sqrt[3]{154}}
Multiply by the Conjugate
\frac{\sqrt[3]{15}\times \sqrt[3]{154^{2}}}{\sqrt[3]{154}\times \sqrt[3]{154^{2}}}
Simplify
\frac{\sqrt[3]{15}\times \sqrt[3]{23716}}{\sqrt[3]{154}\times \sqrt[3]{154^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{15}\times \sqrt[3]{23716}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{15\times 23716}
Calculate the product
\sqrt[3]{355740}
\frac{\sqrt[3]{355740}}{\sqrt[3]{154}\times \sqrt[3]{154^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{154}\times \sqrt[3]{154^{2}}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{154\times 154^{2}}
Calculate the product
\sqrt[3]{154^{3}}
\text{Reduce the index of the radical and exponent with }3
154
\frac{\sqrt[3]{355740}}{154}
x=\frac{\sqrt[3]{355740}}{154}
Alternative Form
x\approx 0.460105
Show Solutions
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