Solve 5x^3x-9 - Socratic AI (ScanMath)

Question

Simplify the expression

5 x^{4} - 9

Evaluate

5 x^{3} \times x - 9

Solution

More Steps

Evaluate

5 x^{3} \times x

Multiply the terms with the same base by adding their exponents

5 x^{3 + 1}

Add the numbers

5 x^{4}

5 x^{4} - 9

Show Solution

x_{1} = - \frac{4 1125}{5}, x_{2} = \frac{4 1125}{5}

Alternative Form

x_{1} \approx - 1.158292, x_{2} \approx 1.158292

Evaluate

5 x^{3} \times x - 9

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

5 x^{3} \times x - 9 = 0

Multiply

More Steps

Multiply the terms

5 x^{3} \times x

Multiply the terms with the same base by adding their exponents

5 x^{3 + 1}

Add the numbers

5 x^{4}

5 x^{4} - 9 = 0

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

5 x^{4} = 0 + 9

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

5 x^{4} = 9

Divide both sides

\frac{5 x ^{4}}{5} = \frac{9}{5}

Divide the numbers

x^{4} = \frac{9}{5}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{9}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{9}{5}

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

\frac{4 9}{4 5}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{4 5}

Multiply by the Conjugate

\frac{3 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{3 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

3 \times 4125

Use n a = mn a^{m} to expand the expression

4 3^{2} \times 4125

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

4 3^{2} \times 125

Calculate the product

41125

\frac{4 1125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 4 5^{3}

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

4 5 \times 5^{3}

Calculate the product

4 5^{4}

Reduce the index of the radical and exponent with 4

5

\frac{4 1125}{5}

x = \pm \frac{4 1125}{5}

Separate the equation into 2 possible cases

x = \frac{4 1125}{5} x = - \frac{4 1125}{5}

Solution

x_{1} = - \frac{4 1125}{5}, x_{2} = \frac{4 1125}{5}

Alternative Form

x_{1} \approx - 1.158292, x_{2} \approx 1.158292

Show Solution