Solve t^2 21t-118=0

Question

Solve the equation

t = \frac{3 52038}{21}

Alternative Form

t \approx 1.777819

Evaluate

t^{2} \times 21 t - 118 = 0

Multiply

More Steps

Evaluate

t^{2} \times 21 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 21

Add the numbers

t^{3} \times 21

Use the commutative property to reorder the terms

21 t^{3}

21 t^{3} - 118 = 0

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

21 t^{3} = 0 + 118

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

21 t^{3} = 118

Divide both sides

\frac{21 t ^{3}}{21} = \frac{118}{21}

Divide the numbers

t^{3} = \frac{118}{21}

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

3 t^{3} = 3 \frac{118}{21}

Calculate

t = 3 \frac{118}{21}

Solution

More Steps

Evaluate

3 \frac{118}{21}

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

\frac{3 118}{3 21}

Multiply by the Conjugate

\frac{3 118 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{3 118 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

3118 \times 3441

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

3 118 \times 441

Calculate the product

352038

\frac{3 52038}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3 2 1^{2}

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

3 21 \times 2 1^{2}

Calculate the product

3 2 1^{3}

Reduce the index of the radical and exponent with 3

21

\frac{3 52038}{21}

t = \frac{3 52038}{21}

Alternative Form

t \approx 1.777819

Show Solution