Solve t^2 4t-6 - ScanMath

Question

Simplify the expression

4 t^{3} - 6

Evaluate

t^{2} \times 4 t - 6

Solution

More Steps

Evaluate

t^{2} \times 4 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 4

Add the numbers

t^{3} \times 4

Use the commutative property to reorder the terms

4 t^{3}

4 t^{3} - 6

Show Solution

Factor the expression

2 (2 t^{3} - 3)

Evaluate

t^{2} \times 4 t - 6

Multiply

More Steps

Evaluate

t^{2} \times 4 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 4

Add the numbers

t^{3} \times 4

Use the commutative property to reorder the terms

4 t^{3}

4 t^{3} - 6

Solution

2 (2 t^{3} - 3)

Show Solution

Find the roots

t = \frac{3 12}{2}

Alternative Form

t \approx 1.144714

Evaluate

t^{2} \times 4 t - 6

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

t^{2} \times 4 t - 6 = 0

Multiply

More Steps

Multiply the terms

t^{2} \times 4 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 4

Add the numbers

t^{3} \times 4

Use the commutative property to reorder the terms

4 t^{3}

4 t^{3} - 6 = 0

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

4 t^{3} = 0 + 6

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

4 t^{3} = 6

Divide both sides

\frac{4 t ^{3}}{4} = \frac{6}{4}

Divide the numbers

t^{3} = \frac{6}{4}

Cancel out the common factor 2

t^{3} = \frac{3}{2}

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

3 t^{3} = 3 \frac{3}{2}

Calculate

t = 3 \frac{3}{2}

Solution

More Steps

Evaluate

3 \frac{3}{2}

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

\frac{3 3}{3 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 34

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

3 3 \times 4

Calculate the product

312

\frac{3 12}{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 12}{2}

t = \frac{3 12}{2}

Alternative Form

t \approx 1.144714

Show Solution