Question

Which of the following shows the square completed in the this equation?

x2 + 3x - 5 = 0
A. (x + 9)2 = 14
B. (x - 3)2 = 8
C. (x + 1.5)2 = 7.25

Answer 1

the way to tackle this type of problem is to first ignore the constant term so we end up with:\[x^2+3x\]next divide the coefficient of x by 2 to form a square expression:\[(x+1.5)^2\]next expand this square expression:\[(x+1.5)^2=x^2+3x+2.25\]now compare it to your original expression which was:\[x^2+3x-5=0\]to make the square expression we found the same as the original equation we need to subtract 7.25, so:\[(x+1.5)^2-7.25=0\]is what we end up with, which can be rearranged to:\[(x+1.5)^2=7.25\]