Solve 8y^2 99y-163

Question

Simplify the expression

792 y^{3} - 163

Evaluate

8 y^{2} \times 99 y - 163

Solution

More Steps

Evaluate

8 y^{2} \times 99 y

Multiply the terms

792 y^{2} \times y

Multiply the terms with the same base by adding their exponents

792 y^{2 + 1}

Add the numbers

792 y^{3}

792 y^{3} - 163

Show Solution

y = \frac{3 59169}{66}

Alternative Form

y \approx 0.590411

Evaluate

8 y^{2} \times 99 y - 163

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

8 y^{2} \times 99 y - 163 = 0

Multiply

More Steps

Multiply the terms

8 y^{2} \times 99 y

Multiply the terms

792 y^{2} \times y

Multiply the terms with the same base by adding their exponents

792 y^{2 + 1}

Add the numbers

792 y^{3}

792 y^{3} - 163 = 0

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

792 y^{3} = 0 + 163

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

792 y^{3} = 163

Divide both sides

\frac{792 y ^{3}}{792} = \frac{163}{792}

Divide the numbers

y^{3} = \frac{163}{792}

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

3 y^{3} = 3 \frac{163}{792}

Calculate

y = 3 \frac{163}{792}

Solution

More Steps

Evaluate

3 \frac{163}{792}

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

\frac{3 163}{3 792}

Simplify the radical expression

More Steps

Evaluate

3792

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

3 8 \times 99

Write the number in exponential form with the base of 2

3 2^{3} \times 99

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

3 2^{3} \times 399

Reduce the index of the radical and exponent with 3

2399

\frac{3 163}{2 3 99}

Multiply by the Conjugate

\frac{3 163 \times 3 9 9 ^{2}}{2 3 99 \times 3 9 9 ^{2}}

Simplify

\frac{3 163 \times 3 3 363}{2 3 99 \times 3 9 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

3163 \times 33363

Multiply the terms

359169 \times 3

Use the commutative property to reorder the terms

3359169

\frac{3 3 59169}{2 3 99 \times 3 9 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

2399 \times 3 9 9^{2}

Multiply the terms

2 \times 99

Multiply the terms

198

\frac{3 3 59169}{198}

Cancel out the common factor 3

\frac{3 59169}{66}

y = \frac{3 59169}{66}

Alternative Form

y \approx 0.590411

Show Solution