Solve x^2-6x+9=(5-2x)^2

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 2, x_{2} = \frac{8}{3}

Alternative Form

x_{1} = 2, x_{2} = 2. \dot{6}

Evaluate

x^{2} - 6 x + 9 = (5 - 2 x)^{2}

Expand the expression

More Steps

Evaluate

(5 - 2 x)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

5^{2} - 2 \times 5 \times 2 x + (2 x)^{2}

Calculate

25 - 20 x + 4 x^{2}

x^{2} - 6 x + 9 = 25 - 20 x + 4 x^{2}

Move the expression to the left side

- 3 x^{2} + 14 x - 16 = 0

Factor the expression

More Steps

Evaluate

- 3 x^{2} + 14 x - 16

Rewrite the expression

- 3 x^{2} + (8 + 6) x - 16

Calculate

- 3 x^{2} + 8 x + 6 x - 16

Rewrite the expression

- x \times 3 x + x \times 8 + 2 \times 3 x - 2 \times 8

Factor out - x from the expression

- x (3 x - 8) + 2 \times 3 x - 2 \times 8

Factor out 2 from the expression

- x (3 x - 8) + 2 (3 x - 8)

Factor out 3 x - 8 from the expression

(- x + 2) (3 x - 8)

(- x + 2) (3 x - 8) = 0

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

3 x - 8 = 0 - x + 2 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 8 = 0

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

3 x = 0 + 8

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

3 x = 8

Divide both sides

\frac{3 x}{3} = \frac{8}{3}

Divide the numbers

x = \frac{8}{3}

x = \frac{8}{3} - x + 2 = 0

Solve the equation for x

More Steps

Evaluate

- x + 2 = 0

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

- x = 0 - 2

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

- x = - 2

Change the signs on both sides of the equation

x = 2

x = \frac{8}{3} x = 2

Solution

x_{1} = 2, x_{2} = \frac{8}{3}

Alternative Form

x_{1} = 2, x_{2} = 2. \dot{6}

Show Solution