Question

can someone help me with completing the square problems... example x^2+8x+7=0

Answer 1

Take the number beside the x (8 in this case), divide it by 2 (4), and square it (16). That 16 is the whole number you want to have at the end \[i.e. \: x^{2} + 8x + 16\] You have a 7 in the way though! How do you turn 7 into 16? You have to add 9. Since it's an equation, you have to add 9 to BOTH sides: \[x^{2} + 8x + 7 + 9 = 0 + 9\]\[x^{2} + 8x + 16 = 9\]You now have a perfect squares on both sides of the equals sign: \[(x + 4)^{2} = 3^{2} \: \: \: \: \: \: (4 \: being \frac{8}{2}, \: and \: \sqrt{16})\] Take the square root of both sides: \[(x + 4) = \pm 9\] Now solve for x (you should get 5, and -13).

Answer 2

Sorry, that last line should be \[(x+4) = \pm 3\] which will give you x = -1, or -7