Q:

Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.1. Divide all terms in the equation by a.2. Subtract the constant (the term without an x) from both sides.3. Add a constant (in terms of a and b) that will complete the square.4. Take the square root of both sides of the equation.5. Solve for x.

Accepted Solution

A:
Answer: The result is the well-known quadratic formula: x = (-b±√(b²-4ac))/(2a)Step-by-step explanation:Start with the standard form quadratic equation: ax² +bx +c = 01. Divide by a x² +(b/a)x +(c/a) = 02. Subtract the constant x² +(b/a)x = -(c/a)3. Complete the square x² +(b/a)x + (b/(2a))² = (b/(2a))²-(c/a) (x +b/(2a))² = (b²-4ac)/(2a)²4. Take the square root x +b/(2a) = ±√(b²-4ac)/(2a)5. Subtract the constant on the left to get x by itself x = (-b±√(b²-4ac))/(2a)