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STEPS ON HOW TO
1. Using Factorization Method
2. Using Formula Method
3. Using Completing the Square Method
4. And about all using Dimixykrrish
STEPS ON HOW TO SOLVE QUADRATIC EQUATION BY
FACTORIZATION METHOD
Example: x2
+ 5x – 6 = 0
Step 1: Firstly note
the coefficient of x2
Coefficient
= 1
Step 2: Find the product
(the
multiplication
of the coefficient of x2 and the constant)
Product
= 1 x - 6
Step 3: Note the sum
Sum
= +5
Step 4: Then find the
factors (two
numbers multiplied together to give the product; -6 and when
Summed gives the Sum; +5)
Factors
= 6 and -1
Step 5: Write the
equation, replacing the sum with the factors
x2
+ 6x – x – 6
Step 6: Group them into
two
(
x2 + 6x) – (x – 6)
Step 7: Find the common
factors of each expression in the bracket
Common
factors = x and -1 respectively.
Step 8: Put the common factors
outside the bracket of their respective expression
x
(x + 6) – 1 (x + 6)
Note:
(Be careful of the
signs here and also note this
whenever you find out that the two numbers inside the bracket are not the same
then you are not correct and you need to start all over again)
Step 9: Pick one of the
expressions in the bracket (since both of them in the bracket are the
same) and the ones outside the
bracket.
Note: Be careful of
the signs at this stage
(x
+ 6) (x – 1)
Step 10: Equate the
expressions to zero
(x
+ 6) (x – 1) = 0
Step 11: Then equate
each of the expression to zero
x+
6 = 0 or x – 1 = 0
Step 12: Take the
constant to the other side across the equal sign (=)
Note: Performing this
task the sign changes
x
= -6 or x = 1
Step 13: Make x the
subject of the formulae (by dividing both sides with the coefficient of x at
that moment)
x
= 6 or x
= 1
1 1
1 1
Step 14: Express the root
as x, x1
-6,
1 (ANSWER)
STEPS ON HOW TO SOLVE QUADRATIC EQUATION BY FORMULA METHOD
Example: 2x2
+ 3x – 5 = 0
Step 1: Write down the
formula
-b+-√b2 – 4ac
2a
Step 2: Write down the values
of the alphabet indicated in the formula from the equation. i.e.
(a = coefficient of x2, b
= coefficient of x and c = constant)
a = 2, b = 3 and c = -5
Step 3: Replace the
alphabet with the values respectively
Note: Be careful of
the signs as they change
-3+-√32 – 4 x 2 x -5
2 x 2
Step 4: Evaluate it (Be careful of
signs)
-3+-√9 + 40
4
-3+-√49
4
-3+-7
4
Step 5: Split the
evaluated value into two, (one carries the positive sign, while the other carries the
negative sign)
-3 + 7 or -3 -
7
4 4
Step 6: Evaluate each
of the expression (Be careful of the signs)
4 or -10
4 4
Step 7: Divide to the
minimum
1 or -5
Step 8: Write the roots
as x, x1
1, -5 (ANSWER)
2
STEPS ON HOW TO SOLVE QUADRATIC EQUATION BY COMPLETING THE
SQUARE METHOD
Example: 2x2 + 5x +3 = 0
Step 1: Divide
through by the coefficient of x2 i.e.
(2)
2x2 + 5x+
3 = 0
2
2 2 2
Step 2: Evaluate
it
x2
+ 5x + 3 = 0
2 2
Step 3: Take the
constant across the equal (=) sign
Note: The sign changes
x2 + 5x = -3
2 2
Step 4: From the
left side (Multiply it by half, take off the square from the x2 and put it
outside
the
bracket and subtract the square from it)
(x
+ 5) 2 x 1 – 5
2 = -3
2 2 4
2
Step 5: Evaluate
it
(x + 5 ) 2 – 25 = -3
4 16
2
Step 6: Try
making x the subject by taking all constants to the other side
(x + 5) 2 =
-3 + 25
4
2 16
Step 7: Evaluate
the right side (the denominator is 16)
(x
+ 5) 2 = -24 + 25
4
16
(x
+ 5 ) 2 = 1
4
16
Step 8: Take the
square of both sides
√x + 5 2 =
√1
4 16
x
+ 5 = +-1
4 4
Step 9: Make x
the subject of the formula
x
= - 5 +-1
4 4
Step 10: Evaluate
it
x
= -5 +-1
4
Step 11: Split the
evaluated value into two, (one carries the positive sign, while the other carries
the
negative sign)
x
= -5 + 1 or x = -5- 1
4
4
Step 12: Evaluate
it
x
= -4 or x = -6
4
4
x = - 1 or x =
- 3
Step 13: Write the
roots as x, x1
1, -3 (ANSWER)
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