The Quadratic Formula: Applying the formula with two solutions

Solve the following equation:

$x^2+5x+4=0$

The parameters are expressed in the quadratic equation as follows:

aX2+bX+c=0

We substitute into the formula:

-5±√(5²-4*1*4) 
          2

-5±√(25-16)
         2

-5±√9
    2

-5±3
   2

The symbol ± means that we have to solve this part twice, once with a plus and a second time with a minus,

This is how we later get two results.

-5-3 = -8
-8/2 = -4

-5+3 = -2
-2/2 = -1

And thus we find out that X = -1, -4

$x_1=-1$ $x_2=-4$

Solve the following equation:

$2x^2-10x-12=0$

Let's recall the quadratic formula:

We'll substitute the given data into the formula:

$x={{-(-10)\pm\sqrt{-10^2-4\cdot2\cdot(-12)}\over 2\cdot2}}$

Let's simplify and solve the part under the square root:

$x={{10\pm\sqrt{100+96}\over 4}}$

$x={{10\pm\sqrt{196}\over 4}}$

$x={{10\pm14\over 4}}$

Now we'll solve using both methods, once with the addition sign and once with the subtraction sign:

$x={{10+14\over 4}} = {24\over4}=6$

$x={{10-14\over 4}} = {-4\over4}=-1$

We've arrived at the solution: X=6,-1

$x_1=6$ $x_2=-1$

Solve the following equation:

$x^2+9x+8=0$

$x_1=-1$ $x_2=-8$

Solve the following equation:

$x^2-3x+2=0$

$x_1=1,x_2=2$

Solve the following:

$x^2+5x+4=0$

$x_1=-1,x_2=-4$

Solve the following equation:

$5x^2-6x+1=0$

$x_1=1,x_2=\frac{1}{5}$

What is the value of X in the following equation?

$X^2+10X+9=0$

$x_1=-1,x_2=-9$

Solve the following equation:

$x^2-4x+4=0$

$x=2$

Solve the following equation:

$4x^2-6x-4=0$

$x_1=2,x_2=-\frac{1}{2}$

Solve the following equation:

$x^2-2x-3=0$

$x_1=3,x_2=-1$

Solve the following equation:

$x^2+5x+6=0$

$x_1=-3,x_2=-2$

Solve the following equation:

$x^2+3x-18=0$

$x_1=3,x_2=-6$

Solve the following equation:

$x^2+10x+21=0$

$x_1=-3,x_2=-7$

Solve for X:

$-2X^2+6X+8=0$

$X_1=4, X_2=-1$

Solve the following equation:

$x^2-x-20=0$

$x_1=-4,x_2=5$

Solve the following equation:

$3x^2+10x-8=0$

$x_1=\frac{2}{3},x_2=-4$

Solve the following equation:

$-2x^2+22x-60=0$

$x_1=5$ $x_2=6$

Solve the following equation:

$x^2+10x+25=0$

$x=-5$

Solve the following equation:

$-x^2+10x-21=0$

$x_1=7,x_2=3$

Solve the equation

$3x^2-39x-90=0$

$x_1=15$ $x_2=-2$