Solve 5000x^2 15x - 16 = 0

Question

Solve the equation

x = \frac{3 90}{75}

Alternative Form

x \approx 0.059752

Evaluate

5000 x^{2} \times 15 x - 16 = 0

Multiply

More Steps

Evaluate

5000 x^{2} \times 15 x

Multiply the terms

75000 x^{2} \times x

Multiply the terms with the same base by adding their exponents

75000 x^{2 + 1}

Add the numbers

75000 x^{3}

75000 x^{3} - 16 = 0

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

75000 x^{3} = 0 + 16

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

75000 x^{3} = 16

Divide both sides

\frac{75000 x ^{3}}{75000} = \frac{16}{75000}

Divide the numbers

x^{3} = \frac{16}{75000}

Cancel out the common factor 8

x^{3} = \frac{2}{9375}

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

3 x^{3} = 3 \frac{2}{9375}

Calculate

x = 3 \frac{2}{9375}

Solution

More Steps

Evaluate

3 \frac{2}{9375}

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

\frac{3 2}{3 9375}

Simplify the radical expression

More Steps

Evaluate

39375

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

3 125 \times 75

Write the number in exponential form with the base of 5

3 5^{3} \times 75

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

3 5^{3} \times 375

Reduce the index of the radical and exponent with 3

5375

\frac{3 2}{5 3 75}

Multiply by the Conjugate

\frac{3 2 \times 3 7 5 ^{2}}{5 3 75 \times 3 7 5 ^{2}}

Simplify

\frac{3 2 \times 5 3 45}{5 3 75 \times 3 7 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 5345

Multiply the terms

390 \times 5

Use the commutative property to reorder the terms

5390

\frac{5 3 90}{5 3 75 \times 3 7 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

5375 \times 3 7 5^{2}

Multiply the terms

5 \times 75

Multiply the terms

375

\frac{5 3 90}{375}

Cancel out the common factor 5

\frac{3 90}{75}

x = \frac{3 90}{75}

Alternative Form

x \approx 0.059752

Show Solution