Taking Square Root:
A pure quadratic equation can be solved by taking the square root of both sides of the equation. Before it taking the square root, the equation must be arranged along with the x2 term isolated on the left- hand side of the equation & its coefficient decreased to 1. There are four steps within solving pure quadratic equations by taking the square root.
Step 1. Using the addition & subtraction axioms and isolate the x2 term on the left-hand side of the equation.
Step 2. Using the multiplication and division axioms, eliminate the coefficient from the x2 term.
Step 3. Take the square root of both sides of the equation.
Step 4. Check the roots.
In taking the square root of both sides of the equation, there are two values which satisfy the equation. For instance, the square roots of x2 are +x and -x because (+x)(+x) = x2 and (-x)(-x) = x2. The square roots of 25 are +5 and -5 since (+5)(+5) = 25 and (-5)(-5) = 25. The two square roots are sometimes denoted by the symbol ±. Therefore, √25 ±5. Because of this property of square roots, both two roots of a pure quadratic equation are the similar except for their sign.
At this point, it should be described that in some cases the result of solving pure quadratic equations is the square root of a negative number. Square roots of negative numbers are known as imaginary numbers and will be discussed later in this section.