Solve x^2 30x - 3 - Socratic AI (ScanMath)

Question

Simplify the expression

30 x^{3} - 3

Evaluate

x^{2} \times 30 x - 3

Solution

More Steps

Evaluate

x^{2} \times 30 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 30

Add the numbers

x^{3} \times 30

Use the commutative property to reorder the terms

30 x^{3}

30 x^{3} - 3

Show Solution

Factor the expression

3 (10 x^{3} - 1)

Evaluate

x^{2} \times 30 x - 3

Multiply

More Steps

Evaluate

x^{2} \times 30 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 30

Add the numbers

x^{3} \times 30

Use the commutative property to reorder the terms

30 x^{3}

30 x^{3} - 3

Solution

3 (10 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 100}{10}

Alternative Form

x \approx 0.464159

Evaluate

x^{2} \times 30 x - 3

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

x^{2} \times 30 x - 3 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 30 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 30

Add the numbers

x^{3} \times 30

Use the commutative property to reorder the terms

30 x^{3}

30 x^{3} - 3 = 0

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

30 x^{3} = 0 + 3

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

30 x^{3} = 3

Divide both sides

\frac{30 x ^{3}}{30} = \frac{3}{30}

Divide the numbers

x^{3} = \frac{3}{30}

Cancel out the common factor 3

x^{3} = \frac{1}{10}

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

3 x^{3} = 3 \frac{1}{10}

Calculate

x = 3 \frac{1}{10}

Solution

More Steps

Evaluate

3 \frac{1}{10}

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

\frac{3 1}{3 10}

Simplify the radical expression

\frac{1}{3 10}

Multiply by the Conjugate

\frac{3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3 1 0^{2}

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

3 10 \times 1 0^{2}

Calculate the product

3 1 0^{3}

Reduce the index of the radical and exponent with 3

10

\frac{3 100}{10}

x = \frac{3 100}{10}

Alternative Form

x \approx 0.464159

Show Solution

X^2 30x 3

Simplify the expression

Factor the expression

Find the roots