Solve (x^2 4x)-(-x^2 5)

Question

Simplify the expression

4 x^{3} + 5 x^{2}

Evaluate

(x^{2} \times 4 x) - (- x^{2} \times 5)

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - (- x^{2} \times 5)

Use the commutative property to reorder the terms

4 x^{3} - (- 5 x^{2})

Solution

4 x^{3} + 5 x^{2}

Show Solution

Factor the expression

x^{2} (4 x + 5)

Evaluate

(x^{2} \times 4 x) - (- x^{2} \times 5)

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - (- x^{2} \times 5)

Use the commutative property to reorder the terms

4 x^{3} - (- 5 x^{2})

Rewrite the expression

4 x^{3} + 5 x^{2}

Rewrite the expression

x^{2} \times 4 x + x^{2} \times 5

Solution

x^{2} (4 x + 5)

Show Solution

Find the roots

x_{1} = - \frac{5}{4}, x_{2} = 0

Alternative Form

x_{1} = - 1.25, x_{2} = 0

Evaluate

(x^{2} \times 4 x) - (- x^{2} \times 5)

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

(x^{2} \times 4 x) - (- x^{2} \times 5) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

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

Use the commutative property to reorder the terms

4 x^{3} - (- 5 x^{2}) = 0

Rewrite the expression

4 x^{3} + 5 x^{2} = 0

Factor the expression

x^{2} (4 x + 5) = 0

Separate the equation into 2 possible cases

x^{2} = 0 4 x + 5 = 0

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

x = 0 4 x + 5 = 0

Solve the equation

More Steps

Evaluate

4 x + 5 = 0

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

4 x = 0 - 5

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

4 x = - 5

Divide both sides

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

Divide the numbers

x = \frac{- 5}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{5}{4}

x = 0 x = - \frac{5}{4}

Solution

x_{1} = - \frac{5}{4}, x_{2} = 0

Alternative Form

x_{1} = - 1.25, x_{2} = 0

Show Solution