# Maths

posted by .

Show proof of deriving the Quadratic Formula from the Quadratic Equation ax^2 + bx + c = O

• Maths -

factor out an a
a(x^2 + b/a) + c = 0

compete the square and don't change the value
a(x^2 + b/a + b^2/4a^2) - a(b^2/4a^2) + c = 0

a(x + b/2a)^2 - b^2/4a + c = 0
(x + b/2a)^2 - b^2/4a^2 + c/a = 0
(x+b/2a)^2 = (b^2 - 4ac)/4a^2
x + b/2a = ±√(b^2-4ac) / 2a
x = (-b ± √(b^2-4ac))/2a

## Similar Questions

r^2+8r=48 First bring the 48 to the other side of the equation r^2+8r-48=0 Now you can use the quadratic formula. x=-b+-sqrt(b^2-(4ac)) ¯¯¯¯¯¯¯2a¯¯¯¯¯¯¯¯¯ So... a=1 b=8 c=-48 Now just plug the numbers into the quadratic …
2. ### Math

Use the quadratic formula to solve each of the following quadratic equations... 1. 2x^2-5x=3 2. 3x^2-2x+1=0 Rearrange the equation in quadratic formula form. 2x^2 -5x -3 = 0 Then use the formula. Tell me what you don't understand about …
3. ### algebra II

I'm quite clueless as to how to solve this. I know the quadratic equation but am not sure how to get this equation into the format to plug in to the quadratic... Solve the quadratic equation using the formula [1/(1+x)]-[1/(3-x)]=(6/35) …
4. ### Algebra

can show me how to do this with out just squaring 3x^(1/2) - x - 6 = 0 how do i do this and solve for x with out just squareing and using quadratic formula. I was never taught the proof of the quadratic formula and would like to know …
5. ### algebra

which quadratic formula would be used to solve the following quadratic equation?
6. ### math

(4.35E-2 - x)(7.56E-2 -x ) ============================ (0.324 + 2x)2 Rearrange to get an expression of the form ax2 + bx + c = 0 and use the quadratic formula (solve for x. This gives: x = 1.05E-2, 0.143 basically i understand they …
7. ### Maths

Show proof of deriving the Quadratic Formula from the Quadratic Equation ax^2 + bx + c = )
8. ### math help how do i do this

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring. −b b^2 − 4ac 2a Use the part of the quadratic formula that you chose above and find its value, given the following …