Solve x 9 = 18 -2x x = 5

Question

Solve the system of equations

x \in \emptyset

Alternative Form

No solution

Evaluate

{x \times 9 = 18 - 2 x \times x 18 - 2 x \times x = 5

Calculate

More Steps

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}

Move the expression to the left side

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Factor the expression

More Steps

Evaluate

9 x - 18 + 2 x^{2}

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

- 6 - x = 0 3 - 2 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

Change the signs on both sides of the equation

x = - 6

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

Calculate

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

{x = - 6 \cup x = \frac{3}{2} 18 - 2 x \times x = 5

Calculate

More Steps

Evaluate

18 - 2 x \times x = 5

Multiply the terms

18 - 2 x^{2} = 5

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

- 2 x^{2} = 5 - 18

Subtract the numbers

- 2 x^{2} = - 13

Change the signs on both sides of the equation

2 x^{2} = 13

Divide both sides

\frac{2 x ^{2}}{2} = \frac{13}{2}

Divide the numbers

x^{2} = \frac{13}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{13}{2}

Simplify the expression

More Steps

Evaluate

\frac{13}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{13}{2}

Multiply by the Conjugate

\frac{13 \times 2}{2 \times 2}

Multiply the numbers

\frac{26}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{26}{2}

x = \pm \frac{26}{2}

Separate the equation into 2 possible cases

x = \frac{26}{2} \cup x = - \frac{26}{2}

{x = - 6 \cup x = \frac{3}{2} x = \frac{26}{2} \cup x = - \frac{26}{2}

Solution

x \in \emptyset

Alternative Form

No solution

Show Solution