Solve (x^2-1)^2=0

$$( x ^ { 2 } - 1 ) ^ { 2 } = 0$$

Solve for x

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-1\right)^{2}.

$$\left(x^{2}\right)^{2}-2x^{2}+1=0$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-2x^{2}+1=0$$

Substitute t for x^{2}.

$$t^{2}-2t+1=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -2 for b, and 1 for c in the quadratic formula.

$$t=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 1\times 1}}{2}$$

Do the calculations.

$$t=\frac{2±0}{2}$$

Solutions are the same.

$$t=1$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.

$$x=-1 x=1$$