Solve 5x^23x^3-x^471

Question

Simplify the expression

15 x^{5} - 71 x^{4}

Evaluate

5 x^{2} \times 3 x^{3} - x^{4} \times 71

Multiply

More Steps

Multiply the terms

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

Multiply the terms

15 x^{2} \times x^{3}

Multiply the terms with the same base by adding their exponents

15 x^{2 + 3}

Add the numbers

15 x^{5}

15 x^{5} - x^{4} \times 71

Solution

15 x^{5} - 71 x^{4}

Show Solution

x^{4} (15 x - 71)

Evaluate

5 x^{2} \times 3 x^{3} - x^{4} \times 71

Multiply

More Steps

Multiply the terms

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

Multiply the terms

15 x^{2} \times x^{3}

Multiply the terms with the same base by adding their exponents

15 x^{2 + 3}

Add the numbers

15 x^{5}

15 x^{5} - x^{4} \times 71

Use the commutative property to reorder the terms

15 x^{5} - 71 x^{4}

Rewrite the expression

x^{4} \times 15 x - x^{4} \times 71

Solution

x^{4} (15 x - 71)

Show Solution

x_{1} = 0, x_{2} = \frac{71}{15}

Alternative Form

x_{1} = 0, x_{2} = 4.7 \dot{3}

Evaluate

5 x^{2} \times 3 x^{3} - x^{4} \times 71

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

5 x^{2} \times 3 x^{3} - x^{4} \times 71 = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

15 x^{2} \times x^{3}

Multiply the terms with the same base by adding their exponents

15 x^{2 + 3}

Add the numbers

15 x^{5}

15 x^{5} - x^{4} \times 71 = 0

Use the commutative property to reorder the terms

15 x^{5} - 71 x^{4} = 0

Factor the expression

x^{4} (15 x - 71) = 0

Separate the equation into 2 possible cases

x^{4} = 0 15 x - 71 = 0

The only way a power can be 0 is when the base equals 0

x = 0 15 x - 71 = 0

Solve the equation

More Steps

Evaluate

15 x - 71 = 0

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

15 x = 0 + 71

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

15 x = 71

Divide both sides

\frac{15 x}{15} = \frac{71}{15}

Divide the numbers

x = \frac{71}{15}

x = 0 x = \frac{71}{15}

Solution

x_{1} = 0, x_{2} = \frac{71}{15}

Alternative Form

x_{1} = 0, x_{2} = 4.7 \dot{3}

Show Solution