complete the square to form a perfect square trinomial x squared+5x+_______
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(5/2)² = 25 / 4
We are basically looking for b² as in
(a + b)² = a² = 2ab + b²
a² = x², so a = x
2ab = 2(x)(b) = 5x
2b = 5, so
b = 5/2
Therefore b² must be (5/2)² = 25 / 4
We are basically looking for b² as in
(a + b)² = a² = 2ab + b²
a² = x², so a = x
2ab = 2(x)(b) = 5x
2b = 5, so
b = 5/2
Therefore b² must be (5/2)² = 25 / 4
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x^(2) + 5x + ---------------------
To use the complete the square method take the 5 from the 5x divide it by 2. Then square it.
5x ---------> (5/2) -------> (5/2)^(2) = (25 / 4)
Therefore you have: x^(2) + 5x + (25 / 4) = [x + (5/2) ] * [x + (5/2)] --------> ANSWER
To use the complete the square method take the 5 from the 5x divide it by 2. Then square it.
5x ---------> (5/2) -------> (5/2)^(2) = (25 / 4)
Therefore you have: x^(2) + 5x + (25 / 4) = [x + (5/2) ] * [x + (5/2)] --------> ANSWER
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add the square of 1/2 the x coefficient, (5/2)² = 25/4
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x^2 + 5x + y = 0
(x + 5/2 )^2 (-5/2)^2
= (x + 5/2 )^2 +25/4
(x + 5/2 )^2 (-5/2)^2
= (x + 5/2 )^2 +25/4