Solve x-c=x^2-c^2

Question

Solve the equation

Solve for x

Solve for c

x = - c + 1 x = c

Evaluate

x - c = x^{2} - c^{2}

Move the expression to the left side

x - c - (x^{2} - c^{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

x - c - x^{2} + c^{2} = 0

Simplify

x - c + c^{2} - x^{2} = 0

Factor the expression

More Steps

Evaluate

x - c + c^{2} - x^{2}

Calculate

- x^{2} + c x - c x + c^{2} + x - c

Rewrite the expression

- x \times x + x c - c x + c \times c + x - c

Factor out - x from the expression

- x (x - c) - c x + c \times c + x - c

Factor out - c from the expression

- x (x - c) - c (x - c) + x - c

Factor out x - c from the expression

(- x - c + 1) (x - c)

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

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

- x - c + 1 = 0 x - c = 0

Solve the equation for x

More Steps

Evaluate

- x - c + 1 = 0

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

- x = 0 - (- c + 1)

Subtract the terms

More Steps

Evaluate

0 - (- c + 1)

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

0 + c - 1

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

c - 1

- x = c - 1

Change the signs on both sides of the equation

x = - c + 1

x = - c + 1 x - c = 0

Solution

More Steps

Evaluate

x - c = 0

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

x = 0 + c

Add the terms

x = c

x = - c + 1 x = c

Show Solution