Solve (x-1)(x+1)=199-287^2

$$(x-1)(x+1)=199- { 287 }^{ 2 }$$

Solve for x (complex solution)

$$x=-\sqrt{82169}i\approx -0-286.65135618i$$

$$x=\sqrt{82169}i\approx 286.65135618i$$

Steps by Finding Square Root

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$x^{2}-1=199-287^{2}$$

Calculate 287 to the power of 2 and get 82369.

$$x^{2}-1=199-82369$$

Subtract 82369 from 199 to get -82170.

$$x^{2}-1=-82170$$

Add 1 to both sides.

$$x^{2}=-82170+1$$

Add -82170 and 1 to get -82169.

$$x^{2}=-82169$$

The equation is now solved.

$$x=\sqrt{82169}i x=-\sqrt{82169}i$$

Steps Using the Quadratic Formula

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$x^{2}-1=199-287^{2}$$

Calculate 287 to the power of 2 and get 82369.

$$x^{2}-1=199-82369$$

Subtract 82369 from 199 to get -82170.

$$x^{2}-1=-82170$$

Add 82170 to both sides.

$$x^{2}-1+82170=0$$

Add -1 and 82170 to get 82169.

$$x^{2}+82169=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 82169 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 82169}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 82169}}{2}$$

Multiply -4 times 82169.

$$x=\frac{0±\sqrt{-328676}}{2}$$

Take the square root of -328676.

$$x=\frac{0±2\sqrt{82169}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{82169}i}{2} when ± is plus.

$$x=\sqrt{82169}i$$

Now solve the equation x=\frac{0±2\sqrt{82169}i}{2} when ± is minus.

$$x=-\sqrt{82169}i$$

The equation is now solved.

$$x=\sqrt{82169}i x=-\sqrt{82169}i$$