Respuesta :
Answer:
The equation is (a+1)² - 56 = 0
Step-by-step explanation:
To solve the quadratic equation a² + 2a - 50 = 5 by completing the square, we can work this way:
First, we find the expansion form of a expanded square equation:
[tex]\boxed{(ax+b)^2=(a^2)x^2+(2ab)x+(b^2)}[/tex]
[tex]a^2+2a-50=5[/tex]
[tex]a^2+2a-55=0[/tex]
Let [tex]a^2+2a-55=0[/tex] is equivalent to [tex](pa+q)^2+r=0[/tex], then:
[tex]a^2+2a-55\equiv(pa+q)^2+r[/tex]
[tex]a^2+2a-55\equiv(p^2)a^2+(2pq)a+(n^2+r)[/tex]
Then we can conclude that:
- [tex]p^2=1\ ...\ [1][/tex]
- [tex]2pq=2\ ...\ [2][/tex]
- [tex]q^2+r=-55\ ...\ [3][/tex]
[1]
[tex]p^2=1[/tex]
[tex]p=1[/tex]
[2]
[tex]2pq=2[/tex]
[tex]2(1)q=2[/tex]
[tex]q=1[/tex]
[3]
[tex]q^2+r=-55[/tex]
[tex]1^2+r=-55[/tex]
[tex]r=-56[/tex]
With the know value of p, q and r, we can conclude that the equation is (a+1)² - 56 = 0
