Solve 3t^2 5t-1 - ScanMath

Question

Simplify the expression

15 t^{3} - 1

Evaluate

3 t^{2} \times 5 t - 1

Solution

More Steps

Evaluate

3 t^{2} \times 5 t

Multiply the terms

15 t^{2} \times t

Multiply the terms with the same base by adding their exponents

15 t^{2 + 1}

Add the numbers

15 t^{3}

15 t^{3} - 1

Show Solution

t = \frac{3 225}{15}

Alternative Form

t \approx 0.40548

Evaluate

3 t^{2} \times 5 t - 1

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

3 t^{2} \times 5 t - 1 = 0

Multiply

More Steps

Multiply the terms

3 t^{2} \times 5 t

Multiply the terms

15 t^{2} \times t

Multiply the terms with the same base by adding their exponents

15 t^{2 + 1}

Add the numbers

15 t^{3}

15 t^{3} - 1 = 0

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

15 t^{3} = 0 + 1

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

15 t^{3} = 1

Divide both sides

\frac{15 t ^{3}}{15} = \frac{1}{15}

Divide the numbers

t^{3} = \frac{1}{15}

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

3 t^{3} = 3 \frac{1}{15}

Calculate

t = 3 \frac{1}{15}

Solution

More Steps

Evaluate

3 \frac{1}{15}

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

\frac{3 1}{3 15}

Simplify the radical expression

\frac{1}{3 15}

Multiply by the Conjugate

\frac{3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3 1 5^{2}

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

3 15 \times 1 5^{2}

Calculate the product

3 1 5^{3}

Reduce the index of the radical and exponent with 3

15

\frac{3 225}{15}

t = \frac{3 225}{15}

Alternative Form

t \approx 0.40548

Show Solution