Solve 4x^(2) 80x-83

Question

Simplify the expression

320 x^{3} - 83

Evaluate

4 x^{2} \times 80 x - 83

Solution

More Steps

Evaluate

4 x^{2} \times 80 x

Multiply the terms

320 x^{2} \times x

Multiply the terms with the same base by adding their exponents

320 x^{2 + 1}

Add the numbers

320 x^{3}

320 x^{3} - 83

Show Solution

x = \frac{3 2075}{20}

Alternative Form

x \approx 0.637739

Evaluate

4 x^{2} \times 80 x - 83

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

4 x^{2} \times 80 x - 83 = 0

Multiply

More Steps

Multiply the terms

4 x^{2} \times 80 x

Multiply the terms

320 x^{2} \times x

Multiply the terms with the same base by adding their exponents

320 x^{2 + 1}

Add the numbers

320 x^{3}

320 x^{3} - 83 = 0

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

320 x^{3} = 0 + 83

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

320 x^{3} = 83

Divide both sides

\frac{320 x ^{3}}{320} = \frac{83}{320}

Divide the numbers

x^{3} = \frac{83}{320}

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

3 x^{3} = 3 \frac{83}{320}

Calculate

x = 3 \frac{83}{320}

Solution

More Steps

Evaluate

3 \frac{83}{320}

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

\frac{3 83}{3 320}

Simplify the radical expression

More Steps

Evaluate

3320

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

3 64 \times 5

Write the number in exponential form with the base of 4

3 4^{3} \times 5

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

3 4^{3} \times 35

Reduce the index of the radical and exponent with 3

435

\frac{3 83}{4 3 5}

Multiply by the Conjugate

\frac{3 83 \times 3 5 ^{2}}{4 3 5 \times 3 5 ^{2}}

Simplify

\frac{3 83 \times 3 25}{4 3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

383 \times 325

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

3 83 \times 25

Calculate the product

32075

\frac{3 2075}{4 3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

435 \times 3 5^{2}

Multiply the terms

4 \times 5

Multiply the terms

20

\frac{3 2075}{20}

x = \frac{3 2075}{20}

Alternative Form

x \approx 0.637739

Show Solution