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.
E. When the sample size increases, because the standard deviation of the distribution of sample means better estimates the population standard deviation for larger sample sizes.
Step-by-step explanation:
T distribution is similar to the normal distribution and is seen when the estimates of the variance are based on the degree of freedom and has a relatively more score in its tail and has a greater change of extreme values.
