Solve 4x^2 - 19x - 5

Question

Factor the expression

(x - 5) (4 x + 1)

Evaluate

4 x^{2} - 19 x - 5

Rewrite the expression

4 x^{2} + (1 - 20) x - 5

Calculate

4 x^{2} + x - 20 x - 5

Rewrite the expression

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

Factor out x from the expression

x (4 x + 1) - 5 \times 4 x - 5

Factor out - 5 from the expression

x (4 x + 1) - 5 (4 x + 1)

Solution

(x - 5) (4 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 0.25, x_{2} = 5

Evaluate

4 x^{2} - 19 x - 5

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

4 x^{2} - 19 x - 5 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 19 x - 5

Rewrite the expression

4 x^{2} + (1 - 20) x - 5

Calculate

4 x^{2} + x - 20 x - 5

Rewrite the expression

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

Factor out x from the expression

x (4 x + 1) - 5 \times 4 x - 5

Factor out - 5 from the expression

x (4 x + 1) - 5 (4 x + 1)

Factor out 4 x + 1 from the expression

(x - 5) (4 x + 1)

(x - 5) (4 x + 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 5 = 0 4 x + 1 = 0

Solve the equation for x

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 + 1 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 1 = 0

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

4 x = 0 - 1

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

4 x = - 1

Divide both sides

\frac{4 x}{4} = \frac{- 1}{4}

Divide the numbers

x = \frac{- 1}{4}

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

x = - \frac{1}{4}

x = 5 x = - \frac{1}{4}

Solution

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

Alternative Form

x_{1} = - 0.25, x_{2} = 5

Show Solution