Solve x^2 5 2x -6

Question

Simplify the expression

52 x^{3} - 6

Evaluate

x^{2} \times 52 x - 6

Solution

More Steps

Evaluate

x^{2} \times 52 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 52

Add the numbers

x^{3} \times 52

Use the commutative property to reorder the terms

52 x^{3}

52 x^{3} - 6

Show Solution

Factor the expression

2 (26 x^{3} - 3)

Evaluate

x^{2} \times 52 x - 6

Multiply

More Steps

Evaluate

x^{2} \times 52 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 52

Add the numbers

x^{3} \times 52

Use the commutative property to reorder the terms

52 x^{3}

52 x^{3} - 6

Solution

2 (26 x^{3} - 3)

Show Solution

Find the roots

x = \frac{3 2028}{26}

Alternative Form

x \approx 0.486836

Evaluate

x^{2} \times 52 x - 6

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

x^{2} \times 52 x - 6 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 52 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 52

Add the numbers

x^{3} \times 52

Use the commutative property to reorder the terms

52 x^{3}

52 x^{3} - 6 = 0

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

52 x^{3} = 0 + 6

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

52 x^{3} = 6

Divide both sides

\frac{52 x ^{3}}{52} = \frac{6}{52}

Divide the numbers

x^{3} = \frac{6}{52}

Cancel out the common factor 2

x^{3} = \frac{3}{26}

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

3 x^{3} = 3 \frac{3}{26}

Calculate

x = 3 \frac{3}{26}

Solution

More Steps

Evaluate

3 \frac{3}{26}

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

\frac{3 3}{3 26}

Multiply by the Conjugate

\frac{3 3 \times 3 2 6 ^{2}}{3 26 \times 3 2 6 ^{2}}

Simplify

\frac{3 3 \times 3 676}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3676

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

3 3 \times 676

Calculate the product

32028

\frac{3 2028}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

326 \times 3 2 6^{2}

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

3 26 \times 2 6^{2}

Calculate the product

3 2 6^{3}

Reduce the index of the radical and exponent with 3

26

\frac{3 2028}{26}

x = \frac{3 2028}{26}

Alternative Form

x \approx 0.486836

Show Solution