Solve r^2 2r-15=0

Question

r^{2} \times 2 r - 15 = 0

Solve the equation

r = \frac{3 60}{2}

Alternative Form

r \approx 1.957434

Evaluate

r^{2} \times 2 r - 15 = 0

Multiply

More Steps

Evaluate

r^{2} \times 2 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 2

Add the numbers

r^{3} \times 2

Use the commutative property to reorder the terms

2 r^{3}

2 r^{3} - 15 = 0

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

2 r^{3} = 0 + 15

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

2 r^{3} = 15

Divide both sides

\frac{2 r ^{3}}{2} = \frac{15}{2}

Divide the numbers

r^{3} = \frac{15}{2}

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

3 r^{3} = 3 \frac{15}{2}

Calculate

r = 3 \frac{15}{2}

Solution

More Steps

Evaluate

3 \frac{15}{2}

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

\frac{3 15}{3 2}

Multiply by the Conjugate

\frac{3 15 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 15 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 34

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

3 15 \times 4

Calculate the product

360

\frac{3 60}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 60}{2}

r = \frac{3 60}{2}

Alternative Form

r \approx 1.957434

Show Solution

Rewrite the equation

4 x^{6} + 12 x^{4} y^{2} + 12 x^{2} y^{4} + 4 y^{6} = 225

Evaluate

r^{2} \times 2 r - 15 = 0

Evaluate

More Steps

Evaluate

r^{2} \times 2 r - 15

Multiply

More Steps

Evaluate

r^{2} \times 2 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 2

Add the numbers

r^{3} \times 2

Use the commutative property to reorder the terms

2 r^{3}

2 r^{3} - 15

2 r^{3} - 15 = 0

Rewrite the expression

2 r^{3} = 15

Evaluate

2 r^{2} \times r = 15

Evaluate

2 (x^{2} + y^{2}) r = 15

Square both sides of the equation

(2 (x^{2} + y^{2}) r)^{2} = 1 5^{2}

Evaluate

(2 (x^{2} + y^{2}))^{2} r^{2} = 1 5^{2}

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

(2 (x^{2} + y^{2}))^{2} (x^{2} + y^{2}) = 1 5^{2}

Use substitution

(4 x^{4} + 8 x^{2} y^{2} + 4 y^{4}) (x^{2} + y^{2}) = 1 5^{2}

Evaluate the power

(4 x^{4} + 8 x^{2} y^{2} + 4 y^{4}) (x^{2} + y^{2}) = 225

Solution

4 x^{6} + 12 x^{4} y^{2} + 12 x^{2} y^{4} + 4 y^{6} = 225

Show Solution

Solve the equation

Rewrite the equation

Graph