Solve x^2=4(2-x)^2

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{4}{3}, x_{2} = 4

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 4

Evaluate

x^{2} = 4 (2 - x)^{2}

Expand the expression

More Steps

Evaluate

4 (2 - x)^{2}

Expand the expression

More Steps

Evaluate

(2 - x)^{2}

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

2^{2} - 2 \times 2 x + x^{2}

Calculate

4 - 4 x + x^{2}

4 (4 - 4 x + x^{2})

Apply the distributive property

4 \times 4 - 4 \times 4 x + 4 x^{2}

Multiply the numbers

16 - 4 \times 4 x + 4 x^{2}

Multiply the numbers

16 - 16 x + 4 x^{2}

x^{2} = 16 - 16 x + 4 x^{2}

Move the expression to the left side

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

Factor the expression

More Steps

Evaluate

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

Reorder the terms

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

Rewrite the expression

- 3 x^{2} + (4 + 12) x - 16

Calculate

- 3 x^{2} + 4 x + 12 x - 16

Rewrite the expression

- x \times 3 x + x \times 4 + 4 \times 3 x - 4 \times 4

Factor out - x from the expression

- x (3 x - 4) + 4 \times 3 x - 4 \times 4

Factor out 4 from the expression

- x (3 x - 4) + 4 (3 x - 4)

Factor out 3 x - 4 from the expression

(- x + 4) (3 x - 4)

(- x + 4) (3 x - 4) = 0

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

- x + 4 = 0 3 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

Change the signs on both sides of the equation

x = 4

x = 4 3 x - 4 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = 4 x = \frac{4}{3}

Solution

x_{1} = \frac{4}{3}, x_{2} = 4

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 4

Show Solution