5 and 1 are the common factor between them
Completing the square
alrighty
minus 31 both sides
x²+12x=-31
take 1/2 of the linear coefient and square it
12 is the linear coefient
12/2=6, (6)²=36
add that to both sides
x²+12x+36=36-31
factor perfect square trinomial
(x+6)²=5
square root both sides, remember to take positive and negative root
x+6=+/-√5
so what you want to write is
x+6=√5 and
x+6=-√5
the solutions
minus 6 both sides
x=-6+√5 and -6-√5
Given:
The quadratic equation is:
To find:
The solution of the given equation in simplest form by using the quadratic formula.
Solution:
If a quadratic equation is 
, then the quadratic formula is:
We have,
Here, 
. Using the quadratic formula, we get
![[\because \sqrt{-a}=i\sqrt{a}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csqrt%7B-a%7D%3Di%5Csqrt%7Ba%7D%5D)
The solutions of the given equations are 
and 
.
Therefore, the correct option is B.
Answer:
x = 8
Step-by-step explanation:
3x - 5 = 2.5x + 3 - (x - 4)
<em>open parentheis</em>
3x - 5 = 2.5x + 3 - x + 4
3x - 5 = 1.5x + 7
<em>subtract 1.5x from both sides of the equation</em>
3x - 1.5x - 5 = 7
1.5x - 5 = 7
<em>add 5 to both sides of the equation</em>
1.5x = 7 + 5
1.5x = 12
<em>divide both sides of the equation by 1.5</em>
1.5x/1.5 = 12/1.5
x = 12/1.5
x = 8
