Solve 4r^(2) 35r-9

Question

Simplify the expression

140 r^{3} - 9

Evaluate

4 r^{2} \times 35 r - 9

Solution

More Steps

Evaluate

4 r^{2} \times 35 r

Multiply the terms

140 r^{2} \times r

Multiply the terms with the same base by adding their exponents

140 r^{2 + 1}

Add the numbers

140 r^{3}

140 r^{3} - 9

Show Solution

r = \frac{3 22050}{70}

Alternative Form

r \approx 0.400594

Evaluate

4 r^{2} \times 35 r - 9

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

4 r^{2} \times 35 r - 9 = 0

Multiply

More Steps

Multiply the terms

4 r^{2} \times 35 r

Multiply the terms

140 r^{2} \times r

Multiply the terms with the same base by adding their exponents

140 r^{2 + 1}

Add the numbers

140 r^{3}

140 r^{3} - 9 = 0

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

140 r^{3} = 0 + 9

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

140 r^{3} = 9

Divide both sides

\frac{140 r ^{3}}{140} = \frac{9}{140}

Divide the numbers

r^{3} = \frac{9}{140}

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

3 r^{3} = 3 \frac{9}{140}

Calculate

r = 3 \frac{9}{140}

Solution

More Steps

Evaluate

3 \frac{9}{140}

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

\frac{3 9}{3 140}

Multiply by the Conjugate

\frac{3 9 \times 3 14 0 ^{2}}{3 140 \times 3 14 0 ^{2}}

Simplify

\frac{3 9 \times 2 3 2450}{3 140 \times 3 14 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 232450

Multiply the terms

322050 \times 2

Use the commutative property to reorder the terms

2322050

\frac{2 3 22050}{3 140 \times 3 14 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

3140 \times 3 14 0^{2}

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

3 140 \times 14 0^{2}

Calculate the product

3 14 0^{3}

Reduce the index of the radical and exponent with 3

140

\frac{2 3 22050}{140}

Cancel out the common factor 2

\frac{3 22050}{70}

r = \frac{3 22050}{70}

Alternative Form

r \approx 0.400594

Show Solution