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Question
12x^{2}\times 7x-10
Simplify the expression
84x^{3}-10
Evaluate
12x^{2}\times 7x-10
Solution
More Steps
Evaluate
12x^{2}\times 7x
Multiply the terms
84x^{2}\times x
Multiply the terms with the same base by adding their exponents
84x^{2+1}
Add the numbers
84x^{3}
84x^{3}-10
Show Solutions
Factor the expression
2\left(42x^{3}-5\right)
Evaluate
12x^{2}\times 7x-10
Multiply
More Steps
Evaluate
12x^{2}\times 7x
Multiply the terms
84x^{2}\times x
Multiply the terms with the same base by adding their exponents
84x^{2+1}
Add the numbers
84x^{3}
84x^{3}-10
Solution
2\left(42x^{3}-5\right)
Show Solutions
Find the roots
x=\frac{\sqrt[3]{8820}}{42}
Alternative Form
x\approx 0.491934
Evaluate
12x^{2}\times 7x-10
To find the roots of the expression,set the expression equal to 0
12x^{2}\times 7x-10=0
Multiply
More Steps
Multiply the terms
12x^{2}\times 7x
Multiply the terms
84x^{2}\times x
Multiply the terms with the same base by adding their exponents
84x^{2+1}
Add the numbers
84x^{3}
84x^{3}-10=0
Move the constant to the right-hand side and change its sign
84x^{3}=0+10
Removing 0 doesn't change the value,so remove it from the expression
84x^{3}=10
Divide both sides
\frac{84x^{3}}{84}=\frac{10}{84}
Divide the numbers
x^{3}=\frac{10}{84}
\text{Cancel out the common factor }2
x^{3}=\frac{5}{42}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{x^{3}}=\sqrt[3]{\frac{5}{42}}
Calculate
x=\sqrt[3]{\frac{5}{42}}
Solution
More Steps
Evaluate
\sqrt[3]{\frac{5}{42}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{5}}{\sqrt[3]{42}}
Multiply by the Conjugate
\frac{\sqrt[3]{5}\times \sqrt[3]{42^{2}}}{\sqrt[3]{42}\times \sqrt[3]{42^{2}}}
Simplify
\frac{\sqrt[3]{5}\times \sqrt[3]{1764}}{\sqrt[3]{42}\times \sqrt[3]{42^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{5}\times \sqrt[3]{1764}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{5\times 1764}
Calculate the product
\sqrt[3]{8820}
\frac{\sqrt[3]{8820}}{\sqrt[3]{42}\times \sqrt[3]{42^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{42}\times \sqrt[3]{42^{2}}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{42\times 42^{2}}
Calculate the product
\sqrt[3]{42^{3}}
\text{Reduce the index of the radical and exponent with }3
42
\frac{\sqrt[3]{8820}}{42}
x=\frac{\sqrt[3]{8820}}{42}
Alternative Form
x\approx 0.491934
Show Solutions
