Solve 4x^2 = 20-11x

Question

4 x^{2} = 20 - 11 x

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 4, x_{2} = 1.25

Evaluate

4 x^{2} = 20 - 11 x

Move the expression to the left side

4 x^{2} - 20 + 11 x = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 20 + 11 x

Reorder the terms

4 x^{2} + 11 x - 20

Rewrite the expression

4 x^{2} + (- 5 + 16) x - 20

Calculate

4 x^{2} - 5 x + 16 x - 20

Rewrite the expression

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

Factor out x from the expression

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

Factor out 4 from the expression

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

Factor out 4 x - 5 from the expression

(x + 4) (4 x - 5)

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

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

4 x - 5 = 0 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 5 = 0

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

4 x = 0 + 5

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

4 x = 5

Divide both sides

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

Divide the numbers

x = \frac{5}{4}

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

Solve the equation for x

More Steps

Evaluate

x + 4 = 0

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

x = 0 - 4

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

x = - 4

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

Solution

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

Alternative Form

x_{1} = - 4, x_{2} = 1.25

Show Solution