Square Root Property

The Square Root Property states that if $$x^2 = k$$ , then $$x = ±√k$$ . This property is used to solve quadratic equations.

Subtract 3 from both sides: $$9r^2 = 9$$ . Then divide by 9: $$r^2 = 1$$ . Finally, take the square root: $$r = ±1$$ .

First, simplify to $$5x^2 = -125$$ , then $$x^2 = -25$$ . The solutions are $$x = 5i$$ and $$x = -5i$$ .

Rearranging gives $$x^2 = -64$$ . The solutions are $$x = 8i$$ and $$x = -8i$$ .

Rearranging gives $$(x-3)^2 = 20$$ . Taking the square root gives $$x - 3 = ±2i√5$$ , so $$x = 3 ± 2i√5$$ .

Taking the square root gives $$x - 3 = ±5$$ . Thus, the solutions are $$x = 8$$ and $$x = -2$$ .

It means that the discriminant (b^2 - 4ac) is less than zero, indicating that the solutions are complex numbers.

The discriminant is the part of the quadratic formula under the square root: $$b^2 - 4ac$$ . It determines the nature of the roots.

If the discriminant is greater than zero (b^2 - 4ac > 0), the equation has two distinct real solutions.

The general form is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and $$a ≠ 0$$ .