How do you solve using the completing the square method x^2 +8x+14=0 x2+8x+14=0?

1 Answer
EZ as pi
Jun 16, 2016

x = -2.586 " or " -5.414x=−2.586 or −5.414

Explanation:

NOte that when you square a binomial there is always a particular pattern for the answer.

(x - 3)^2 = x^2 -6x + 9 " " (ax^2 + bx + c)(x−3)2=x2−6x+9 (ax2+bx+c)
As long as a = 1a=1, then there is always the same relationship between b and c.
"(half of b)"^2 (half of b)2gives c. " "c. check (-6 ÷ 2)^2 = (-3)^2 = 9(−6÷2)2=(−3)2=9

In x^2 + 8x + 14 = 0x2+8x+14=0 we would like the left side to be written as

"(binomial)"^2(binomial)2

  1. Move the constant to the right side.
    x^2 + 8x " " = -14x2+8x =−14

  2. Add the missing term to both sides (b/2)^2(b2)2
    x^2 color(blue)+ 8x + color(red)16 = -14 + color(red)16x2+8x+16=−14+16

This is the part that is COMPLETING THE SQUARE.
(Add in what is missing to form a perfect square)

  1. The left side is the answer to the square of a binomial;
    (x color(blue)+ 4)^2 = 2(x+4)2=2

  2. Find the square root of each side.
    x + 4 = +-sqrt2x+4=±√2

  3. Solve for xx twice, once with +sqrt2+√2, once with -sqrt2−√2
    x = +sqrt2 -4 " or " x = -sqrt2 -4x=+√2−4 or x=−√2−47
    x = -2.586 " or " -5.414x=−2.586 or −5.414

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