Solve 7x^53x-2 - ScanMath

Question

Simplify the expression

21 x^{6} - 2

Evaluate

7 x^{5} \times 3 x - 2

Solution

More Steps

Evaluate

7 x^{5} \times 3 x

Multiply the terms

21 x^{5} \times x

Multiply the terms with the same base by adding their exponents

21 x^{5 + 1}

Add the numbers

21 x^{6}

21 x^{6} - 2

Show Solution

x_{1} = - \frac{6 2 \times 2 1 ^{5}}{21}, x_{2} = \frac{6 2 \times 2 1 ^{5}}{21}

Alternative Form

x_{1} \approx - 0.675774, x_{2} \approx 0.675774

Evaluate

7 x^{5} \times 3 x - 2

To find the roots of the expression,set the expression equal to 0

7 x^{5} \times 3 x - 2 = 0

Multiply

More Steps

Multiply the terms

7 x^{5} \times 3 x

Multiply the terms

21 x^{5} \times x

Multiply the terms with the same base by adding their exponents

21 x^{5 + 1}

Add the numbers

21 x^{6}

21 x^{6} - 2 = 0

Move the constant to the right-hand side and change its sign

21 x^{6} = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

21 x^{6} = 2

Divide both sides

\frac{21 x ^{6}}{21} = \frac{2}{21}

Divide the numbers

x^{6} = \frac{2}{21}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 6 \frac{2}{21}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{21}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 2}{6 21}

Multiply by the Conjugate

\frac{6 2 \times 6 2 1 ^{5}}{6 21 \times 6 2 1 ^{5}}

The product of roots with the same index is equal to the root of the product

\frac{6 2 \times 2 1 ^{5}}{6 21 \times 6 2 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

621 \times 6 2 1^{5}

The product of roots with the same index is equal to the root of the product

6 21 \times 2 1^{5}

Calculate the product

6 2 1^{6}

Reduce the index of the radical and exponent with 6

21

\frac{6 2 \times 2 1 ^{5}}{21}

x = \pm \frac{6 2 \times 2 1 ^{5}}{21}

Separate the equation into 2 possible cases

x = \frac{6 2 \times 2 1 ^{5}}{21} x = - \frac{6 2 \times 2 1 ^{5}}{21}

Solution

x_{1} = - \frac{6 2 \times 2 1 ^{5}}{21}, x_{2} = \frac{6 2 \times 2 1 ^{5}}{21}

Alternative Form

x_{1} \approx - 0.675774, x_{2} \approx 0.675774

Show Solution