# What are the formula and factor of this :s^2+3=6s

1
by dechavezarthur

2014-06-21T09:28:47+08:00
You can use completing the square method or the quadratic formula to find the roots and get the factor. Note the standard form of quadratic equation Ax² + Bx + C = 0.

By completing the square:

s² + 3 = 6s
s² - 6s = -3          Equation 1

Next get (B/2A)² :

(B/2A)² = {-6/2(1)}²
= (-3)²
= 9 ............ADD THIS TO BOTH SIDES OF EQUATION 1

We will have:

s² - 6s + 9 = -3 + 9
Left side of this equation is now a perfect square; thus factorable..

(s-3)² = 6
take the square root of both side to find your "s"
s-3 = √6

s = √6 + 3     FIRST ROOT                   ANSWER

s = - √6 + 3   SECOND ROOT                ANSWER

You can also use the quadratic formula: and you will get the same answer.

S = { -B +/- √ B² - 4AC } / 2A

S₁ = negative B PLUS the square root of the quantity B²-4AC all over 2A...for root 1.
S₂    = negative B MINUS the square root of the quantity B²-4AC all over 2A...for root 2