Completing the Square...help..please.?

Question

This was a bonus question on my test that i know i got wrong. can someone please show me how to do with steps please.

ax^2+bx+c=0

thanks

thats confusing to look at.....

Answer 1

a (x² + (b/a)x + c/a) = 0
x² + (b/a)x + c/a = 0
(x² + (b/a)x + b² /4a²) + c/a - b²/4a² = 0
( x + (b/2a) )² = b²/4a² - c/a
( x + (b/2a) )² = (b² - 4ac) / 4a²
x + (b/2a) = ±√ (b² - 4ac) / 2a
x = - (b/2a) ± √ (b² - 4ac) / 2a
x = [- b ± √(b² - 4ac) ] / 2a

Answer 2

O I hated these in math
Ok so anyways, its easier to explain with an example. x^2+4x-8=0.
First move the constant to the other side (x^2+4x=8)
Then make sure the leading coefficient is 1 (in this problem, it is)
Then divide the middle number by 2 and square it and add this number to both sides of the equation (x^2+4x+4=4)
Then factor the equation ((x+2)^2=4)
Then take the square root of both sides (x+2=2)
Then solve (x=0)

Answer 3

ax^2+bx+c=0
To complete the square, subtract C, divide both sides by a and add a blank to the equation to make a perfect square binomial. x^2+bx/a+____/a=-c/a
To make it a perfect square binomial, divide the middle term (bx) by 2 and square the result. (bx/2a)^2= b^2/4a^2. Since, we can't add something at random without adding it to both sides, x^2+b/a(x)+b^2/4a^2=-c/a+b^2/4a^2
Factor x^2+b/a(x)+b^2/4a^2 to get (x+b/2a)^2. On the other side of the equation, find the common denominator of a and 4a^2. Multiply -c/a by 4a. The equation should look like this, (x+b/2a)^2= b^2-4ac/4a^2. Find the square root of both sides, x+b/2a=(b^2-4ac)square root/4a^2
Subract b/2a from the left side, and you should end up with the Quadractic formula. x=-b(plus/minus)(Square root of)b^2-4ac/2a.

Answer 4

SOLVING A QUADRATIC EQUATION IN X BY COMPLETING THE SQUARE

1)if the coefficient of x^2 is 1, go to Step 2. Otherwise, divide both sides of the equation by the coefficient of x^2
2)Isolate all variable terms on one side of the equation.
3)complete the square for the resulting binomial by adding the square of half of the coefficient of x to both sides of the equation.
4)factor the resuling perfect square trinomial and write it as the square of a binomial
5)use the square root property(If b is a real number and if a^2=b, then a= plus or minus the squareroot of b)to solve for x.

Answer 5

try to turn that into (x+d)(x+e) = ax^2+bx+c
what would that make d and e equal to?