There are different ways to solve a quadratic equation, the main ones that i'm thinking about right now are:
1) factor the equation as a product:
ex: x^2+ 4x + 3 =0
(x+3) (x+1) = 0
x=-3 and x=-1 are the solutions.
To find (x+p) and (x+q) you have to think that (p+q )have to be equal to the number that is multiplied by x, in my example it was 4 (3+1=4), (p times q) have to be equal to the last number of the quadratic equation, the one that is not multiplied by any x, that in my example is 3 (3 x 1= 3)
2) The other way to solve a quadratic function is by using a formula:
given: ax^2 +bx +c=0
x= (-b +/- <span>√(b^2 -</span> 4ac)) / 2a
ex: 3x^2 + 4x -2=0
x= (-4 +/- √16-4(3)(-2)) / 6= (-4 +/- √16+24)/6= (-4 +/- <span>√40) / 6
now there are 2 possibilities: x= (-4+</span><span>√40) /6
and
x= (-4 - </span><span>√40) / 6
I hope the examples were clear enough also if i did't get very nice numbers. Look closely to the sings + and -, they are very important</span>
9x-22=23+4x
Now you subtract 4x from both sides to get the variable on one side..
5x-22=23
Now solve as you would solve a 2 step equation.
5x=45
Divide both sides by 5 to get the variable by itself.
x=9
3x + y = 15
5x3y = 11
This is an example of a system of equations.
A system of equations is two or more equations that can be graphed, as the solution that satisfies both equations will be the point where the lines intersect on a graph.
Desmos is a graphing calculator, and thus it allows you to visualize this system.
6(3x+5)
6*3x=18x
6*5=30
<u>18x+30</u> is your answer! I hope this helped! :)
