Solve 35a^2 32a-16=0

Question

Solve the equation

a = \frac{3 4900}{70}

Alternative Form

a \approx 0.242643

Evaluate

35 a^{2} \times 32 a - 16 = 0

Multiply

More Steps

Evaluate

35 a^{2} \times 32 a

Multiply the terms

1120 a^{2} \times a

Multiply the terms with the same base by adding their exponents

1120 a^{2 + 1}

Add the numbers

1120 a^{3}

1120 a^{3} - 16 = 0

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

1120 a^{3} = 0 + 16

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

1120 a^{3} = 16

Divide both sides

\frac{1120 a ^{3}}{1120} = \frac{16}{1120}

Divide the numbers

a^{3} = \frac{16}{1120}

Cancel out the common factor 16

a^{3} = \frac{1}{70}

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

3 a^{3} = 3 \frac{1}{70}

Calculate

a = 3 \frac{1}{70}

Solution

More Steps

Evaluate

3 \frac{1}{70}

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

\frac{3 1}{3 70}

Simplify the radical expression

\frac{1}{3 70}

Multiply by the Conjugate

\frac{3 7 0 ^{2}}{3 70 \times 3 7 0 ^{2}}

Simplify

\frac{3 4900}{3 70 \times 3 7 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

370 \times 3 7 0^{2}

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

3 70 \times 7 0^{2}

Calculate the product

3 7 0^{3}

Reduce the index of the radical and exponent with 3

70

\frac{3 4900}{70}

a = \frac{3 4900}{70}

Alternative Form

a \approx 0.242643

Show Solution