Answer:
quadratic formula, completing the square, factorisation
Explanation:
Quadratic formula:
x = (-b ± √(b² - 4ac) ÷ 2a)
where a is the value of the first coefficient, b is value of the second and c is value of the constant.
x = ((-b ± √(b² - 4ac)) ÷ 2a)
= (( -16± √((-16)² - 4(8)(3)) ÷ 2(8))
= ((-16 ± √(256 - 96)) ÷ 16)
= (-16 ± √(160)) ÷ 16
= -1 ± (√10)/4
Completing the square:
divide through by 8
x² + 2x + 3/8 = 0
1) put the x, not ^2, in parenthesis.
(x + ) = 0
2) half the coefficient (2) of x. that is 1. Put that into same parenthesis.
(x + 1) = 0
3) we have (x + 1)
4) square this and multiply out. (x + 1)² = x² + x + x +4 = x² +2x + 1
5) this looks just like the original equation (x² + 2x + 3/8) except for +1. What do we have to do to get back to original? 1 – (3/8) = 5/8. We have to subtract 5/8
6) now we have (x + 1)² – 5/8 =0
7) (x + 1)² = 5/8
8) (x + 1) = ± √(5/8)
9) x = ± √(5/8) - 1
= -1 ± (√10)/4
Factorisation:
(8x (- (2√10)) + 8) = 0,
8x = -8 + (2√10)),
x = -1 + (√10)/4
(x ( + (√10)/4 + 1) = 0
x = -1 - (√10)/4