SOLUTION: Can you show me step by step how to complete the square? 1.) 3t^2 + 24t-13 2.) 4s^2+s+2

Question 181102: Can you show me step by step how to complete the square?
1.) 3t^2 + 24t-13
2.) 4s^2+s+2

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
complete the square?
1.) 3t^2 + 24t-13
The coefficient of t^2 has to be 1, divide each term by 3, results:
t^2 + 8t - = 0
:
t^2 + 8t + ___ =
Find the term that will complete the square; square half of the coefficient of t
.5*8=4; 4^2=16; add to both sides
t^2 + 8t + 16 = + 16
:
t^2 + 8t + 9 = + ; change 16 to thirds
:
(t + 4)^2 =
Find the square root of both sides:
t + 4 = +/-
subtract 4 from both sides, we have two solutions
t = -4 +
and
t = -4 -
:
:
;
2.) 4s^2+s+2
Divide each term by 4 to make the coefficient of s^2 = 1, results
s^2 + s + = 0
s^2 + s + ___ = -
Complete the square, half of (1/4) = (1/8); (1/8)^2 = (1/64)
s^2 + s + = - +
s^2 + s + = - +
s^2 + s + = -
(s + )^2 = -
s + = +/-
s = - +/-
Extract square root of -1 and square root of (1/64)
s = - +/-i
Can also be written
s =
and
s =
:
:
Was this sufficient steps?

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