Respuesta :
Answer:
1) [tex] x^2 -4x +(\frac{4}{2})^2 -\frac{5}{2} - (\frac{4}{2})^2[/tex]
[tex] (x-2)^2 -\frac{5}{2} -4=(x-2)^2 -\frac{13}{2}[/tex]
2) [tex] x^2 -3x +(\frac{3}{2})^2 +\frac{1}{2} - (\frac{3}{2})^2[/tex]
[tex] (x-\frac{3}{2})^2 +\frac{1}{2} -\frac{9}{4}=(x-\frac{3}{2})^2 -\frac{7}{4}[/tex]
3) [tex] x^2 +\frac{9}{2}x +(\frac{9}{4})^2 -\frac{15}{4} - (\frac{9}{4})^2[/tex]
[tex] (x+\frac{9}{4})^2 -\frac{15}{4} -\frac{81}{16}=(x+\frac{9}{4})^2 -\frac{141}{16}[/tex]
4) [tex] c^2 -\frac{5}{4}c +(\frac{5}{8})^2 -\frac{139}{200} - (\frac{5}{8})^2[/tex]
[tex] (c-\frac{5}{8})^2 -\frac{139}{200} -\frac{25}{64}=(c-\frac{5}{8})^2 -\frac{1737}{1600}[/tex]
5) [tex] n^2 +\frac{1}{4}n +(\frac{1}{8})^2 +\frac{5}{8} - (\frac{1}{8})^2[/tex]
[tex] (n+\frac{1}{8})^2 +\frac{5}{8} -\frac{1}{64}=(n+\frac{1}{8})^2 +\frac{39}{64}[/tex]
Step-by-step explanation:
1. −2x^2 + 8x + 5
For this case we can begin dividing all the terms by -2 and we got:
[tex] x^2 -4x -\frac{5}{2}[/tex
And if we complete the square we got:
[tex] x^2 -4x +(\frac{4}{2})^2 -\frac{5}{2} - (\frac{4}{2})^2[/tex]
[tex] (x-2)^2 -\frac{5}{2} -4=(x-2)^2 -\frac{13}{2}[/tex]
2. 2.5x^2 − 7.5x + 1.25
For this case we can begin dividing all the terms by 2.5 and we got:
[tex] x^2 -3x + \frac{1}{2}[/tex]
And if we complete the square we got:
[tex] x^2 -3x +(\frac{3}{2})^2 +\frac{1}{2} - (\frac{3}{2})^2[/tex]
[tex] (x-\frac{3}{2})^2 +\frac{1}{2} -\frac{9}{4}=(x-\frac{3}{2})^2 -\frac{7}{4}[/tex]
3. 4 / 3x ^2 + 6x − 5
For this case we can begin dividing all the terms by 4/3 and we got:
[tex] x^2 + \frac{9}{2}x - \frac{15}{4}[/tex]
And if we complete the square we got:
[tex] x^2 +\frac{9}{2}x +(\frac{9}{4})^2 -\frac{15}{4} - (\frac{9}{4})^2[/tex]
[tex] (x+\frac{9}{4})^2 -\frac{15}{4} -\frac{81}{16}=(x+\frac{9}{4})^2 -\frac{141}{16}[/tex]
4. 1000c^2 − 1250c + 695
For this case we can begin dividing all the terms by 1000 and we got:
[tex] c^2 - \frac{5}{4}c + \frac{139}{200}[/tex]
And if we complete the square we got:
[tex] c^2 -\frac{5}{4}c +(\frac{5}{8})^2 +\frac{139}{200} - (\frac{5}{8})^2[/tex]
[tex] (c-\frac{5}{8})^2 -\frac{139}{200} -\frac{25}{64}=(c-\frac{5}{8})^2 -\frac{487}{1600}[/tex]
5. 8n^2 + 2n + 5
For this case we can begin dividing all the terms by 8 and we got:
[tex] n^2 + \frac{1}{4}x + \frac{5}{8}[/tex]
And if we complete the square we got:
[tex] n^2 +\frac{1}{4}n +(\frac{1}{8})^2 +\frac{5}{8} - (\frac{1}{8})^2[/tex]
[tex] (n+\frac{1}{8})^2 +\frac{5}{8} -\frac{1}{64}=(n+\frac{1}{8})^2 +\frac{39}{64}[/tex]
