Solve x^212x-45 - ScanMath

Question

Simplify the expression

12 x^{3} - 45

Evaluate

x^{2} \times 12 x - 45

Solution

More Steps

Evaluate

x^{2} \times 12 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 12

Add the numbers

x^{3} \times 12

Use the commutative property to reorder the terms

12 x^{3}

12 x^{3} - 45

Show Solution

Factor the expression

3 (4 x^{3} - 15)

Evaluate

x^{2} \times 12 x - 45

Multiply

More Steps

Evaluate

x^{2} \times 12 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 12

Add the numbers

x^{3} \times 12

Use the commutative property to reorder the terms

12 x^{3}

12 x^{3} - 45

Solution

3 (4 x^{3} - 15)

Show Solution

Find the roots

x = \frac{3 30}{2}

Alternative Form

x \approx 1.553616

Evaluate

x^{2} \times 12 x - 45

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

x^{2} \times 12 x - 45 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 12 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 12

Add the numbers

x^{3} \times 12

Use the commutative property to reorder the terms

12 x^{3}

12 x^{3} - 45 = 0

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

12 x^{3} = 0 + 45

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

12 x^{3} = 45

Divide both sides

\frac{12 x ^{3}}{12} = \frac{45}{12}

Divide the numbers

x^{3} = \frac{45}{12}

Cancel out the common factor 3

x^{3} = \frac{15}{4}

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

3 x^{3} = 3 \frac{15}{4}

Calculate

x = 3 \frac{15}{4}

Solution

More Steps

Evaluate

3 \frac{15}{4}

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

\frac{3 15}{3 4}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

315 \times 232

Multiply the terms

330 \times 2

Use the commutative property to reorder the terms

2330

\frac{2 3 30}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 30}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 30}{2}

x = \frac{3 30}{2}

Alternative Form

x \approx 1.553616

Show Solution