Solve 25x(x+1)=-4

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 0.8, x_{2} = - 0.2

Evaluate

25 x (x + 1) = - 4

Expand the expression

More Steps

Evaluate

25 x (x + 1)

Apply the distributive property

25 x \times x + 25 x \times 1

Multiply the terms

25 x^{2} + 25 x \times 1

Any expression multiplied by 1 remains the same

25 x^{2} + 25 x

25 x^{2} + 25 x = - 4

Move the expression to the left side

25 x^{2} + 25 x + 4 = 0

Factor the expression

More Steps

Evaluate

25 x^{2} + 25 x + 4

Rewrite the expression

25 x^{2} + (20 + 5) x + 4

Calculate

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

Rewrite the expression

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

Factor out 5 x from the expression

5 x (5 x + 4) + 5 x + 4

Factor out 5 x + 4 from the expression

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

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

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

5 x + 1 = 0 5 x + 4 = 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 = - \frac{1}{5} 5 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 4 = 0

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

5 x = 0 - 4

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

5 x = - 4

Divide both sides

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

Divide the numbers

x = \frac{- 4}{5}

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

x = - \frac{4}{5}

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

Solution

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

Alternative Form

x_{1} = - 0.8, x_{2} = - 0.2

Show Solution