Solve 9-5x-4x^2=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{9}{4}, x_{2} = 1

Alternative Form

x_{1} = - 2.25, x_{2} = 1

Evaluate

9 - 5 x - 4 x^{2} = 0

Factor the expression

More Steps

Evaluate

9 - 5 x - 4 x^{2}

Rewrite the expression

9 + (4 - 9) x - 4 x^{2}

Calculate

9 + 4 x - 9 x - 4 x^{2}

Rewrite the expression

9 + 4 x - x \times 9 - x \times 4 x

Factor out - x from the expression

9 + 4 x - x (9 + 4 x)

Factor out 9 + 4 x from the expression

(1 - x) (9 + 4 x)

(1 - x) (9 + 4 x) = 0

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

1 - x = 0 9 + 4 x = 0

Solve the equation for x

More Steps

Evaluate

1 - x = 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

Change the signs on both sides of the equation

x = 1

x = 1 9 + 4 x = 0

Solve the equation for x

More Steps

Evaluate

9 + 4 x = 0

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

4 x = 0 - 9

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

4 x = - 9

Divide both sides

\frac{4 x}{4} = \frac{- 9}{4}

Divide the numbers

x = \frac{- 9}{4}

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

x = - \frac{9}{4}

x = 1 x = - \frac{9}{4}

Solution

x_{1} = - \frac{9}{4}, x_{2} = 1

Alternative Form

x_{1} = - 2.25, x_{2} = 1

Show Solution