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.

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 = 0

1. Divide by a

x² +(b/a)x +(c/a) = 0

2. 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)²

4. 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)

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

c

step-by-step explanation: