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How to Solve a Formula for the Indicated Variable?

TopIn mathematics there is wide variety of general formulae. These formulas when directly used, evaluates us the value of desired variable. For instance, let us consider an example of Quadratic Formula for any Quadratic Equation Ax2 + Bx + C = 0 that can be given as follows:

x = (- B ± √D) /2 A,

Where, 'D' is called as determinant and whose value can be given as: D = B2 – 4 AC.

Let us learn how to solve a formula for the indicated variable through an example:

Example: Suppose we have a quadratic equation 2 x2 – 8 x + 5 = 0. Solve this equation for value of 'x'?

Solution: Here in this equation “x” is the indicated variable for which we need to solve quadratic formula. When given equation is compared by the general equation, we see that A = 2, B = - 8 and C = 5. Formula we have to solve for 'x' can be given as follows:

x = (- B - √D) /2 a and x = (- B + √D) /2 A or

x = (- B - √ (B2 – 4 A C)) /2 A and x = (- B + √(B2 – 4 A C)) /2 A,

Substituting values of A, B and C in above formula we get the value of indicted variable 'x' as:

x = (8 - √ (82 – 4 * 2 * 5)) /2 * 2 and x = (8 + √(82 – 4 * 2 * 5)) /2 * 2,

x = (8 - √24) /4 and x = (8 + √24) /4

x = (4 - √6) /2 and x = (4 - √6) /2

Thus we get two values for indicated variable 'x'.