Solve x^3=x^(2) 3x-5

Question

Solve the equation

x = \frac{3 20}{2}

Alternative Form

x \approx 1.357209

Evaluate

x^{3} = x^{2} \times 3 x - 5

Multiply

More Steps

Evaluate

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

x^{3} = 3 x^{3} - 5

Move the expression to the left side

x^{3} - (3 x^{3} - 5) = 0

Subtract the terms

More Steps

Evaluate

x^{3} - (3 x^{3} - 5)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{3} - 3 x^{3} + 5

Subtract the terms

More Steps

Evaluate

x^{3} - 3 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 3) x^{3}

Subtract the numbers

- 2 x^{3}

- 2 x^{3} + 5

- 2 x^{3} + 5 = 0

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

- 2 x^{3} = 0 - 5

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

- 2 x^{3} = - 5

Change the signs on both sides of the equation

2 x^{3} = 5

Divide both sides

\frac{2 x ^{3}}{2} = \frac{5}{2}

Divide the numbers

x^{3} = \frac{5}{2}

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

3 x^{3} = 3 \frac{5}{2}

Calculate

x = 3 \frac{5}{2}

Solution

More Steps

Evaluate

3 \frac{5}{2}

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

\frac{3 5}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 5 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 34

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

3 5 \times 4

Calculate the product

320

\frac{3 20}{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 20}{2}

x = \frac{3 20}{2}

Alternative Form

x \approx 1.357209

Show Solution

Solve the equation

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