Solving Quadratic Equations

-Angelina Melendez Negron & Abigail Mercado

We will show you the steps on how to solve 2 quadratic equations

What are the steps for (x^2-2x+1=0)

SIMPLE EQUATION

Step 1:

Find the factors of 1 that when you add equals to -2


Factors of 1:


  • -1,-1 = -2

Step 2:

Plug in x in 2 set of parentheses

(x ) ( )

Step 3:

Plug in the 2 factors from step 1 that equalled to -2 into the parenthesis (-1,-1)

(x-1) (x-1)

Step 4:

make each set of parenthesis equal 0

x-1=0

x-1=0

Step 5:

try to get everything on one side

x-1=0 (ADD 1 ON BOTH SIDES)

-1+1=cancels out to 0

1+0= 1

x=1


x-1=0 (ADD 1 ON BOTH SIDES)

-1+1=cancels out to 0

1+0=1

x=1

Step 5:

plug into brackets

{1,1} <answer

What are the steps for (7x^2+21x-28=0)

Step 1:

You have to multiply 7 and -28 to get x^2 alone


7x-28=-196

Step 2:

Now we have to find the factors of -196 that when you add equal to 21


Factors-

28,-7=21

Step 3:

Rewrite the equation (plug in factors)



7x^2+28x-7x-28=0

Step 4:

Find the factors of the first set and plug in


|7x^2+28x|-7x-28=0


  • take out a x from 7x^2 which would be 7x
  • put 7x outside of the parenthesis
  • put the remainder x inside the parenthesis 7x(x)
  • divide 28 by 7 which gives you 4
  • put the 4 inside the parenthesis which would be 7x(x+4)

Step 5:

Find the factors of the second set and plug in


7x^2+28x|-7x-28|=0

  • take out a x from -7x which would be -7
  • put -7 outside the new set of parentheses
  • put the remainder x inside the parenthesis -7(x)
  • divide -28 by -7 which gives you 4
  • put the 4 inside the parenthesis which would be -7(x+4)

Step 6:

Combine the 2 sets that we did in step 4 and step 5


7x(x+4)-7(x+4)


Step 7:

Put the 2 outside numbers from both sets and combine them into 1 set


7x(x+4)-7(x+4)


(7x-7)

Step 8:

Since the 2 closed parenthesis have the numbers in them we make it as one


7x(x+4)-7(x+4)


(x+4)

Step 9:

Put the 2 parenthesis that we created in step 7 and step 8 side by side


(7x-7)(x+4)

Step 10:

Put both parenthesis to equal 0


7x-7=0

x+4=0

Step 11:

Solve the equations that we made in step 10


7x-7=0

!get everything to 1 side!

add 7 on both sides

0+7=7

-7+7=0

7x=7

divide by 7 on both sides

7x/7= x

7/7=1

so now we know that one of our solutions is x=1


x+4=0

!get everything to 1 side!

subtract 4 on both sides

0-4=-4

4-4=0

so now we know that the second solution is x=-4

FINAL STEP:

Plug both of our solutions that we got in step 11 into brackets


{1,4} <answer


By:Angelina & Abigail