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

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 1, x_{2} = 4

Evaluate

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

Calculate

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

Swap the sides

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

Expand the expression

More Steps

Evaluate

2 - (x - 2)^{2}

Evaluate the power

More Steps

Evaluate

- (x - 2)^{2}

Expand the expression

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

Expand the expression

- x^{2} + 4 x - 4

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

Subtract the numbers

- 2 - x^{2} + 4 x

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

Move the expression to the left side

- 4 - x^{2} + 5 x = 0

Factor the expression

More Steps

Evaluate

- 4 - x^{2} + 5 x

Reorder the terms

- 4 + 5 x - x^{2}

Rewrite the expression

- 4 + (4 + 1) x - x^{2}

Calculate

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

Rewrite the expression

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

Factor out - 4 from the expression

- 4 (1 - x) + x - x \times x

Factor out x from the expression

- 4 (1 - x) + x (1 - x)

Factor out 1 - x from the expression

(- 4 + x) (1 - x)

(- 4 + x) (1 - x) = 0

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

- 4 + x = 0 1 - x = 0

Solve the equation for x

More Steps

Evaluate

- 4 + x = 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

x = 4 1 - x = 0

Solve the equation for x

More Steps

Evaluate

1 - x = 0

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

- x = 0 - 1

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

- x = - 1

Change the signs on both sides of the equation

x = 1

x = 4 x = 1

Solution

x_{1} = 1, x_{2} = 4

Show Solution