Answer:
81/4
Step-by-step explanation:
Given the equation x^2 – 9x + 38 = 0
Subtract 38 from both sides
x^2 – 9x + 38 - 38= 0 - 38
x^2 - 9x = -38
Next is to complete the square, to do this we will add the square of the half of coefficient of x to both sides as shown;
Coefficient of x is - 9
Half of -9 will be (-9/2)
Squaring the result will give (-9/2)² = 81/4
Hence the number that would have to be added to "complete the
square" is 81/4 to have;
x^2 - 9x + 81/4= -38 + 81/4
(x-9/2)² = -38 + 81/4
Hence the required value is 81/4
