Solve 16x^2 52x -300

Question

Simplify the expression

832 x^{3} - 300

Evaluate

16 x^{2} \times 52 x - 300

Solution

More Steps

Evaluate

16 x^{2} \times 52 x

Multiply the terms

832 x^{2} \times x

Multiply the terms with the same base by adding their exponents

832 x^{2 + 1}

Add the numbers

832 x^{3}

832 x^{3} - 300

Show Solution

Factor the expression

4 (208 x^{3} - 75)

Evaluate

16 x^{2} \times 52 x - 300

Multiply

More Steps

Evaluate

16 x^{2} \times 52 x

Multiply the terms

832 x^{2} \times x

Multiply the terms with the same base by adding their exponents

832 x^{2 + 1}

Add the numbers

832 x^{3}

832 x^{3} - 300

Solution

4 (208 x^{3} - 75)

Show Solution

Find the roots

x = \frac{3 50700}{52}

Alternative Form

x \approx 0.711758

Evaluate

16 x^{2} \times 52 x - 300

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

16 x^{2} \times 52 x - 300 = 0

Multiply

More Steps

Multiply the terms

16 x^{2} \times 52 x

Multiply the terms

832 x^{2} \times x

Multiply the terms with the same base by adding their exponents

832 x^{2 + 1}

Add the numbers

832 x^{3}

832 x^{3} - 300 = 0

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

832 x^{3} = 0 + 300

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

832 x^{3} = 300

Divide both sides

\frac{832 x ^{3}}{832} = \frac{300}{832}

Divide the numbers

x^{3} = \frac{300}{832}

Cancel out the common factor 4

x^{3} = \frac{75}{208}

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

3 x^{3} = 3 \frac{75}{208}

Calculate

x = 3 \frac{75}{208}

Solution

More Steps

Evaluate

3 \frac{75}{208}

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

\frac{3 75}{3 208}

Simplify the radical expression

More Steps

Evaluate

3208

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 26

Write the number in exponential form with the base of 2

3 2^{3} \times 26

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 326

Reduce the index of the radical and exponent with 3

2326

\frac{3 75}{2 3 26}

Multiply by the Conjugate

\frac{3 75 \times 3 2 6 ^{2}}{2 3 26 \times 3 2 6 ^{2}}

Simplify

\frac{3 75 \times 3 676}{2 3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

375 \times 3676

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

3 75 \times 676

Calculate the product

350700

\frac{3 50700}{2 3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

2326 \times 3 2 6^{2}

Multiply the terms

2 \times 26

Multiply the terms

52

\frac{3 50700}{52}

x = \frac{3 50700}{52}

Alternative Form

x \approx 0.711758

Show Solution