x^2 - 8x - 29 ≡ (x+a)^2 + b
find the value of a and b I have started this question and i guess you complete the square. alhough i was wondering if it is a -8x
then (x-4)^2 is it plus or minus 4^2 ?
cheers :)
maths a/s question help?
2009-01-04 2:34 pm
回答 (3)
2009-01-04 2:45 pm
✔ 最佳答案
x² - 8x - 29 ≡ (x+a)² + bx² - 8x - 29 ≡ x² + 2ax + a² + b
Equate coefficients of x²:
1 = 1
Equate coefficients of x:
-8 = 2a
a = -4
Equate constant terms:
-29 = a² + b
-29 = 16 + b
b = -45
a = -4
b = -45
2009-01-04 10:57 pm
x^2 - 8x - 29 â¡ (x + a)^2 + b
x^2 - 4x - 4x - 29 â¡ (x + a)^2 + b
x^2 - 4x - 4x + 16 - 29 - 16 â¡ (x + a)^2 + b
(x^2 - 4x) - (4x - 16) - 45 â¡ (x + a)^2 + b
x(x - 4) - 4(x - 4) - 45 â¡ (x + a)^2 + b
(x - 4)(x - 4) - 45 â¡ (x + a)^2 + b
(x - 4)^2 - 45 â¡ (x + a)^2 + b
a = -4
b = -45
x^2 - 4x - 4x - 29 â¡ (x + a)^2 + b
x^2 - 4x - 4x + 16 - 29 - 16 â¡ (x + a)^2 + b
(x^2 - 4x) - (4x - 16) - 45 â¡ (x + a)^2 + b
x(x - 4) - 4(x - 4) - 45 â¡ (x + a)^2 + b
(x - 4)(x - 4) - 45 â¡ (x + a)^2 + b
(x - 4)^2 - 45 â¡ (x + a)^2 + b
a = -4
b = -45
2009-01-04 10:47 pm
x^2 - 8x - 29 = ( x+ a )^2 + b
x^2 - 8x - -29 = x^2 + 2ax + a^2 + b
now compare coefficient
-8x = 2ax
2a = -8
a = -8/2
a = -4
a^2 + b = -29
(-4)^2 + b = -29
16 + b = -29
b = -29 - 16
b = -45
x^2 - 8x - -29 = x^2 + 2ax + a^2 + b
now compare coefficient
-8x = 2ax
2a = -8
a = -8/2
a = -4
a^2 + b = -29
(-4)^2 + b = -29
16 + b = -29
b = -29 - 16
b = -45
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