Solve 5x^2-4x-1 - ScanMath

Question

Factor the expression

(x - 1) (5 x + 1)

Evaluate

5 x^{2} - 4 x - 1

Rewrite the expression

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

Calculate

5 x^{2} + x - 5 x - 1

Rewrite the expression

x \times 5 x + x - 5 x - 1

Factor out x from the expression

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

Factor out - 1 from the expression

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

Solution

(x - 1) (5 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 0.2, x_{2} = 1

Evaluate

5 x^{2} - 4 x - 1

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

5 x^{2} - 4 x - 1 = 0

Factor the expression

More Steps

Evaluate

5 x^{2} - 4 x - 1

Rewrite the expression

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

Calculate

5 x^{2} + x - 5 x - 1

Rewrite the expression

x \times 5 x + x - 5 x - 1

Factor out x from the expression

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

Factor out - 1 from the expression

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

Factor out 5 x + 1 from the expression

(x - 1) (5 x + 1)

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

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

x - 1 = 0 5 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 5 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 1 = 0

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

5 x = 0 - 1

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

5 x = - 1

Divide both sides

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

Divide the numbers

x = \frac{- 1}{5}

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

x = - \frac{1}{5}

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

Solution

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

Alternative Form

x_{1} = - 0.2, x_{2} = 1

Show Solution