Solve this equation by completing the square
p2 - 8p + 21 = 6….when solving by completing the square, all constant terms should be on the right side
p2 - 8p + 21 – 21 = 6 – 21….subtracting 21 from both sides
p2 - 8p = -15
Always do these steps when completing the square: divide the coefficient (8) of the second term by 2 and
then add the square of your answer to both sides of the equation 8/2 = 4 then 42 = 16
p2 - 8p + 42 = -15 + 42…..on the left side you have created a perfect square trinomial ax² -2ab + b² = (x-b)(x-b) = (x-b)²
p2 -2(1)(4)p + 42 = -15 + 16……….proving it’s a perfect square trinomial
(p - 4)2 = 1……to get rid of your square, you have to find the square root of both sides
√
= ±√1 ….once you find the square root of a number it’s always ± of the square root.
Examples: √6 = ± 8; √1
= ±10; √ 6 = ±6
p – = ± 1……. ±1 means +1 and -1
p – 4 = 1 or p – 4 = -1
p = 5 or p = 3