Answer:
Let's do an example first and then summerize what are the techniques to complete the square for quadratic equation in order to solve for x. -2x^2 + 5x + 12 = 0 -2x^2 + 5x = -12 -2 (x^2 - 5/2 x) = -12 so 2ab = 5/2 x ("2ab" refers to the formula (a+b)^2 = a^2 + 2ab + b^2 or (a+b)^2 = a^2 - 2ab + b^2 ) Since a=1 (because x^2 is the a^2 in the formula), we get 2*1*b = 2b = 5/2 x, so b = 5/4 That means to complete the square we will add "b^2" (which is (5/4)^2 here) and then subtract (5/4)^2 in the parenthesis: -2 [ x^2 - 5/2 x + (5/4)^2 - (5/4)^2 ] = -12 Now that is same as -2 (x - 5/4 )^2 + (-2) * (-5/4)^2 = -12 To simplify it we follow these steps: -2 (x - 5/4 )^2 + 2 * 25/16 = -12 -2 (x - 5/4 )^2 + 25/8 = -12 Multiply both sides of the equation by 8 we get this: -16 (x-5/4)^2 +25 = -96 then -16 (x-5/4)^2 = -121 Techniques summerization: To complete the square for quadratic equation in order to solve for x, first we need to move the terms without x (which is "c" in the "ax^2+bx+c=0" form) to the right side of the equation. Then we divide both sides of the equation by "a" in the "ax^2+bx+c=0" equation. Through the formula (a+b)^2 = a^2 + 2ab + b^2 or (a+b)^2 = a^2 - 2ab + b^2 we will then figure out the value of "b", so then we know what is the b^2 we need to add then subtract. Finally just simplify the equation. Hope this helps.
Step-by-step explanation:
Answer:
rhombus, rectangle, trapezoid
Step-by-step explanation:
can i get the crown pls pls pls?
All you need to do is that Step-by-step explanation:
There are a total of 4 quarters and 16 nickels.
Answer:
x=7 and y=4
Step-by-step explanation:
I will use the elimination method:
Since the co-efficient of both y's are the same number but different signs we add the 2 equations to eliminate the y:
3x + y =25
+ + +
2x - y = 10
Simplify:
5x=35
Divide both sides by 5:
5x÷5=35÷5
Simplify:
x=7
Substitute this into either equation 1 or 2 ( I chose 1):
3(7) + y = 25
21 + y = 25
Subtract 21 from both sides and simplify to get y:
21+y-21=25-21
y=4
Therefore x=7 and y=4
