Solve 175r^2 150r-33=0

Question

Solve the equation

$Solve for r$

r = \frac{3 53900}{350}

Alternative Form

r \approx 0.107927

Evaluate

175 r^{2} \times 150 r - 33 = 0

Multiply

More Steps

Evaluate

175 r^{2} \times 150 r

Multiply the terms

26250 r^{2} \times r

Multiply the terms with the same base by adding their exponents

26250 r^{2 + 1}

Add the numbers

26250 r^{3}

26250 r^{3} - 33 = 0

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

26250 r^{3} = 0 + 33

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

26250 r^{3} = 33

Divide both sides

\frac{26250 r ^{3}}{26250} = \frac{33}{26250}

Divide the numbers

r^{3} = \frac{33}{26250}

Cancel out the common factor 3

r^{3} = \frac{11}{8750}

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

3 r^{3} = 3 \frac{11}{8750}

Calculate

r = 3 \frac{11}{8750}

Solution

More Steps

Evaluate

3 \frac{11}{8750}

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

\frac{3 11}{3 8750}

Simplify the radical expression

More Steps

Evaluate

38750

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

3 125 \times 70

Write the number in exponential form with the base of 5

3 5^{3} \times 70

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

3 5^{3} \times 370

Reduce the index of the radical and exponent with 3

5370

\frac{3 11}{5 3 70}

Multiply by the Conjugate

\frac{3 11 \times 3 7 0 ^{2}}{5 3 70 \times 3 7 0 ^{2}}

Simplify

\frac{3 11 \times 3 4900}{5 3 70 \times 3 7 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 34900

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

3 11 \times 4900

Calculate the product

353900

\frac{3 53900}{5 3 70 \times 3 7 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

5370 \times 3 7 0^{2}

Multiply the terms

5 \times 70

Multiply the terms

350

\frac{3 53900}{350}

r = \frac{3 53900}{350}

Alternative Form

r \approx 0.107927

Show Solution

Rewrite the equation

Rewrite in rectangular form

875 0^{2} x^{6} + 3 \times 875 0^{2} x^{4} y^{2} + 3 \times 875 0^{2} x^{2} y^{4} + 875 0^{2} y^{6} = 121

Evaluate

175 r^{2} \times 150 r - 33 = 0

Evaluate

More Steps

Evaluate

175 r^{2} \times 150 r - 33

Multiply

More Steps

Evaluate

175 r^{2} \times 150 r

Multiply the terms

26250 r^{2} \times r

Multiply the terms with the same base by adding their exponents

26250 r^{2 + 1}

Add the numbers

26250 r^{3}

26250 r^{3} - 33

26250 r^{3} - 33 = 0

Rewrite the expression

26250 r^{3} = 33

Evaluate

26250 r^{2} \times r = 33

Evaluate

26250 (x^{2} + y^{2}) r = 33

Square both sides of the equation

(26250 (x^{2} + y^{2}) r)^{2} = 3 3^{2}

Evaluate

(26250 (x^{2} + y^{2}))^{2} r^{2} = 3 3^{2}

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

(26250 (x^{2} + y^{2}))^{2} (x^{2} + y^{2}) = 3 3^{2}

Use substitution

(2625 0^{2} x^{4} + 2625 0^{2} \times 2 x^{2} y^{2} + 2625 0^{2} y^{4}) (x^{2} + y^{2}) = 3 3^{2}

Evaluate the power

(2625 0^{2} x^{4} + 2625 0^{2} \times 2 x^{2} y^{2} + 2625 0^{2} y^{4}) (x^{2} + y^{2}) = 1089

Divide both sides of the equation by 9

(875 0^{2} x^{4} + 875 0^{2} \times 2 x^{2} y^{2} + 875 0^{2} y^{4}) (x^{2} + y^{2}) = 121

Solution

875 0^{2} x^{6} + 3 \times 875 0^{2} x^{4} y^{2} + 3 \times 875 0^{2} x^{2} y^{4} + 875 0^{2} y^{6} = 121

Show Solution

175r^2 150r 33=0

Solve the equation

$Solve for r$

Rewrite the equation

Rewrite in rectangular form

Graph