Solving Quadratic Equations using the Square Root Property

The Square Root Property states that if $$x^2 = a$$ , then $$x = \text{±}\sqrt{a}$$ , where a is a non-negative number.

Take the square root of both sides: $$x - 7 = \text{±} \sqrt{99}$$ . Then, solve for x: $$x = 7 \text{±} 3\sqrt{11}$$ .

The solutions are $$x = 7$$ and $$x = -7$$ .

First, divide both sides by 2: $$(2x - 4)^2 = 16$$ . Then, take the square root: $$2x - 4 = \text{±} 4$$ . Solve for x to get $$x = 0$$ and $$x = 4$$ .

Subtract 3 from both sides: $$9r^2 = 9$$ . Divide by 9: $$r^2 = 1$$ . Take the square root: $$r = 1$$ and $$r = -1$$ .

Subtract 12 from both sides: $$x^2 = -7$$ . Since the square of a real number cannot be negative, the solutions are $$x = \text{±} i \sqrt{7}$$ .

Isolate the squared term on one side of the equation.

It means that the expression under the square root (the discriminant) is negative.

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

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