Solve x^2-(x-3)*x 9=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 0, x_{2} = \frac{27}{8}

Alternative Form

x_{1} = 0, x_{2} = 3.375

Evaluate

x^{2} - (x - 3) x \times 9 = 0

Multiply the terms

More Steps

Evaluate

(x - 3) x \times 9

Use the commutative property to reorder the terms

(x - 3) \times 9 x

Multiply the terms

9 x (x - 3)

x^{2} - 9 x (x - 3) = 0

Expand the expression

More Steps

Evaluate

x^{2} - 9 x (x - 3)

Multiply the terms

More Steps

Evaluate

- 9 x (x - 3)

Apply the distributive property

- 9 x \times x - (- 9 x \times 3)

Multiply the terms

- 9 x^{2} - (- 9 x \times 3)

Multiply the numbers

- 9 x^{2} - (- 27 x)

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^{2} + 27 x

x^{2} - 9 x^{2} + 27 x

Subtract the terms

More Steps

Evaluate

x^{2} - 9 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 9) x^{2}

Subtract the numbers

- 8 x^{2}

- 8 x^{2} + 27 x

- 8 x^{2} + 27 x = 0

Factor the expression

More Steps

Evaluate

- 8 x^{2} + 27 x

Rewrite the expression

- x \times 8 x + x \times 27

Factor out - x from the expression

- x (8 x - 27)

- x (8 x - 27) = 0

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

8 x - 27 = 0 - x = 0

Solve the equation for x

More Steps

Evaluate

8 x - 27 = 0

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

8 x = 0 + 27

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

8 x = 27

Divide both sides

\frac{8 x}{8} = \frac{27}{8}

Divide the numbers

x = \frac{27}{8}

x = \frac{27}{8} - x = 0

Solve the equation for x

x = \frac{27}{8} x = 0

Solution

x_{1} = 0, x_{2} = \frac{27}{8}

Alternative Form

x_{1} = 0, x_{2} = 3.375

Show Solution

Solve the quadratic equation

Graph