Solve t^212t - 11 = 0

Question

Solve the equation

t = \frac{3 198}{6}

Alternative Form

t \approx 0.971413

Evaluate

t^{2} \times 12 t - 11 = 0

Multiply

More Steps

Evaluate

t^{2} \times 12 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 12

Add the numbers

t^{3} \times 12

Use the commutative property to reorder the terms

12 t^{3}

12 t^{3} - 11 = 0

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

12 t^{3} = 0 + 11

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

12 t^{3} = 11

Divide both sides

\frac{12 t ^{3}}{12} = \frac{11}{12}

Divide the numbers

t^{3} = \frac{11}{12}

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

3 t^{3} = 3 \frac{11}{12}

Calculate

t = 3 \frac{11}{12}

Solution

More Steps

Evaluate

3 \frac{11}{12}

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

\frac{3 11}{3 12}

Multiply by the Conjugate

\frac{3 11 \times 3 1 2 ^{2}}{3 12 \times 3 1 2 ^{2}}

Simplify

\frac{3 11 \times 2 3 18}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 2318

Multiply the terms

3198 \times 2

Use the commutative property to reorder the terms

23198

\frac{2 3 198}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 3 1 2^{2}

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

3 12 \times 1 2^{2}

Calculate the product

3 1 2^{3}

Reduce the index of the radical and exponent with 3

12

\frac{2 3 198}{12}

Cancel out the common factor 2

\frac{3 198}{6}

t = \frac{3 198}{6}

Alternative Form

t \approx 0.971413

Show Solution