Solve (x-5)(4x+11)

Question

Simplify the expression

4 x^{2} - 9 x - 55

Evaluate

(x - 5) (4 x + 11)

Apply the distributive property

x \times 4 x + x \times 11 - 5 \times 4 x - 5 \times 11

Multiply the terms

More Steps

Evaluate

x \times 4 x

Use the commutative property to reorder the terms

4 x \times x

Multiply the terms

4 x^{2}

4 x^{2} + x \times 11 - 5 \times 4 x - 5 \times 11

Use the commutative property to reorder the terms

4 x^{2} + 11 x - 5 \times 4 x - 5 \times 11

Multiply the numbers

4 x^{2} + 11 x - 20 x - 5 \times 11

Multiply the numbers

4 x^{2} + 11 x - 20 x - 55

Solution

More Steps

Evaluate

11 x - 20 x

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

(11 - 20) x

Subtract the numbers

- 9 x

4 x^{2} - 9 x - 55

Show Solution

x_{1} = - \frac{11}{4}, x_{2} = 5

Alternative Form

x_{1} = - 2.75, x_{2} = 5

Evaluate

(x - 5) (4 x + 11)

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

(x - 5) (4 x + 11) = 0

Separate the equation into 2 possible cases

x - 5 = 0 4 x + 11 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 4 x + 11 = 0

Solve the equation

More Steps

Evaluate

4 x + 11 = 0

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

4 x = 0 - 11

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

4 x = - 11

Divide both sides

\frac{4 x}{4} = \frac{- 11}{4}

Divide the numbers

x = \frac{- 11}{4}

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

x = - \frac{11}{4}

x = 5 x = - \frac{11}{4}

Solution

x_{1} = - \frac{11}{4}, x_{2} = 5

Alternative Form

x_{1} = - 2.75, x_{2} = 5

Show Solution