Solve x 9 = 18 -2x x

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 6, x_{2} = \frac{3}{2}

Alternative Form

x_{1} = - 6, x_{2} = 1.5

Evaluate

x \times 9 = 18 - 2 x \times x

Use the commutative property to reorder the terms

9 x = 18 - 2 x \times x

Multiply the terms

9 x = 18 - 2 x^{2}

Swap the sides

18 - 2 x^{2} = 9 x

Move the expression to the left side

18 - 2 x^{2} - 9 x = 0

Factor the expression

More Steps

Evaluate

18 - 2 x^{2} - 9 x

Reorder the terms

18 - 9 x - 2 x^{2}

Rewrite the expression

18 + (- 12 + 3) x - 2 x^{2}

Calculate

18 - 12 x + 3 x - 2 x^{2}

Rewrite the expression

6 \times 3 - 6 \times 2 x + x \times 3 - x \times 2 x

Factor out 6 from the expression

6 (3 - 2 x) + x \times 3 - x \times 2 x

Factor out x from the expression

6 (3 - 2 x) + x (3 - 2 x)

Factor out 3 - 2 x from the expression

(6 + x) (3 - 2 x)

(6 + x) (3 - 2 x) = 0

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

3 - 2 x = 0 6 + x = 0

Solve the equation for x

More Steps

Evaluate

3 - 2 x = 0

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

- 2 x = 0 - 3

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

- 2 x = - 3

Change the signs on both sides of the equation

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

x = \frac{3}{2} 6 + x = 0

Solve the equation for x

More Steps

Evaluate

6 + x = 0

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

x = 0 - 6

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

x = - 6

x = \frac{3}{2} x = - 6

Solution

x_{1} = - 6, x_{2} = \frac{3}{2}

Alternative Form

x_{1} = - 6, x_{2} = 1.5

Show Solution