translate book. (tugas5)

Assignment 5.
Square Equation ( translate book )
Reference: Erlangga, page 182 – 193
7.1 Definition of square equation
Look at some equation below
a) P^2-4 = 0
b) q^2 – 9q = 0
Every equation above only have one variable, and the highest power of variable is two. Equation
a) 2x^2 + 3x -2 = 0; a=2, b=3, c=-2
b) x^2-6x+9=0; a=1 b=-6 c=9
solving or roots of square equation of x are changer of x such that equation become correct.

Example 7.1
I equation x square minus 16 times equals zero
If x change by 4 so 4^2-16=0,
16 – 16=0 ( is correct )
If x change by -4 so -4^2-16=0,
16 – 16=0 ( is correct )
And so roots of equation x^2 – 16=0 is correct for 4 or -4
If x change by 2 so (2^2)-16=0,
4-16=-12(wrong)
If x change by 2 so (2^2)-16=0,
4-16=-12(wrong)
So 2 or (-2) are not roots of equation x^2-16=0. Actually roots of equation x^2-16=0 onli 4 or (-4). Lets try to other value of x!
There are three ways to solve square equation, there are by factoring , by complete the perfect square, and by using formula.

7.2 Solve Square equation by Factoring
We have known that multiply by zero will be product zero. On the contrary, a multiply if product zero, surely one its number that multiplied is zero.
Example:
If 3x=0 so that x=0
If 5(x-4)=0 so x-4=0
If pq=0 so p=0 or q=0

Example 7.2
1. Solve the square equation below :
a. x^2 +2x -3 =0
b. 3x^2=5x+2
c. 2x^2+6x=0
answers :
a. . x^2 +2x -3 =0
(x-1) (x+3)=0
X=1 or x=-3
b. 3x^2=5x+2
3x^2-5x-2=0
(3x+1)(x-2)=0
X=-1/3 or x=2
c. 2x^2+6x=0
2x(x+3)=0
2x=0 or x+3=0
X=0 or x=-3

2.Determine solving set of 9x^2 -4 =0
ANSWERS :
(3x-2)(3x+2)=0
X=-2/3 or x=2/3

Exercise 1
1. determine changer variable at every equation !
a. 3(3x-2)=0
b. p(p-4)=0
c. 2p(p+3)=0
d. (t-3)(t+1)=0
e. 5(t-2)(t+3)=0
f. (3n-4)^2=0
g. (-7n+1)(6n-5)=0
h. –(2m-5)(2m+5)=0

2. Solve equations by factoring!
a. 2x^2-x=0
b. 4x-6x^2=0
c. 9y^2-25=0
d. 16t^2-49=0
e. 3x^2-17x-6=0

3. Determine the solving sets of these equations
a. x^2+x=0
b. x^2-25=0
c. 9x^2-1=0
d. x^2+12x+35=0

4. Known 4 is one of solving roots of equation x^2+5=a(3x-a-2). Determine value of a.

5. Determine value of b if 5 is one of solving of equation 2x^2+x+b=0. Determine also the other solving.

7.2.1 Square equation in form of fraction
Oftentimes square equation writes by fraction form. To making to come easy, solve the equation, initially we must omit the denominator, by multiply by LCM (Least Common Multiply) of denominator.

Conclusion.
Steps to solving the square equation by complete prefect square are:
1. Place coefficient that have variable at left side and constant at right side.
2. Coefficient of x^2 must one
3. Add two side by square of half coefficient of x so that left side come perfect square