Solving Quadratic Equations using Factoring: One sided equations

Let's first expand the parentheses using the formula:

$a(x+b)=ax+ab$

$(2\times x)+(2\times4)+8=0$

$2x+8+8=0$

Next, we will substitute in our terms accordingly:

$2x+16=0$

Then, we will move the 16 to the left-hand side, keeping the appropriate sign:

$2x=-16$

Finally, we divide both sides by 2:

$\frac{2x}{2}=-\frac{16}{2}$

$x=-8$

We open the parentheses according to the formula:

$a(x+b)=ax+ab$

$5\times x+5\times3=0$

$5x+15=0$

We will move the 15 to the right section and keep the corresponding sign:

$5x=-15$

Divide both sections by 5

$\frac{5x}{5}=\frac{-15}{5}$

$x=-3$

Let's open the parentheses using the distributive property and use the formula:

$a(x+b)=ax+ab$

$40+5a-2a-14=56$

We'll substitute the terms accordingly:

$26+3a=56$

We'll move 26 to the right side and keep the appropriate sign:

$3a=56-26$

$3a=30$

We'll divide both sides by 3:

$\frac{3a}{3}=\frac{30}{3}$

$a=10$

We will use the extended division rule and the formula:

$a(x+b)=ax+ab$

$-42x+36+5+8x=0$

Let's input the appropriate terms:

$-34x+41=0$

We'll move -34x to the right side and maintain the appropriate sign:

$41=34x$

Let's divide both sides by 34:

$\frac{41}{34}=\frac{34x}{34}$

$\frac{41}{34}=x$

We'll convert the simple fraction to a mixed fraction:

$x=1\frac{7}{34}$