Solve 26x^242x-9=0

Question

Solve the equation

x = \frac{3 3 \times 36 4 ^{2}}{364}

Alternative Form

x \approx 0.201995

Evaluate

26 x^{2} \times 42 x - 9 = 0

Multiply

More Steps

Evaluate

26 x^{2} \times 42 x

Multiply the terms

1092 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1092 x^{2 + 1}

Add the numbers

1092 x^{3}

1092 x^{3} - 9 = 0

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

1092 x^{3} = 0 + 9

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

1092 x^{3} = 9

Divide both sides

\frac{1092 x ^{3}}{1092} = \frac{9}{1092}

Divide the numbers

x^{3} = \frac{9}{1092}

Cancel out the common factor 3

x^{3} = \frac{3}{364}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{3}{364}

Calculate

x = 3 \frac{3}{364}

Solution

More Steps

Evaluate

3 \frac{3}{364}

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

\frac{3 3}{3 364}

Multiply by the Conjugate

\frac{3 3 \times 3 36 4 ^{2}}{3 364 \times 3 36 4 ^{2}}

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

\frac{3 3 \times 36 4 ^{2}}{3 364 \times 3 36 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

3364 \times 3 36 4^{2}

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

3 364 \times 36 4^{2}

Calculate the product

3 36 4^{3}

Reduce the index of the radical and exponent with 3

364

\frac{3 3 \times 36 4 ^{2}}{364}

x = \frac{3 3 \times 36 4 ^{2}}{364}

Alternative Form

x \approx 0.201995

Show Solution