Respuesta :

Subtract 49 from both sides to get equation into [tex]a x^{2} +bx+c=0[/tex] form:

[tex] a^{2} -10a-24=0[/tex]

Then factor:

[tex](a-12)(a+2)=0[/tex]

Solutions corresponding to these factors are [tex]a=12[/tex] and [tex]a=-2[/tex].

Answer:

[tex]a_{1}= 12[/tex] and [tex]a_{2}= -2[/tex].

Step-by-step explanation:

We are given the equation,

[tex]a^2-10a+25=49[/tex]

i.e. [tex]a^2-10a=49-25[/tex]

i.e. [tex]a^2-10a=24[/tex]

i.e. [tex]a^2-10a-24=0[/tex]

i.e. [tex](a-12)(a+2)=0[/tex]

i.e. [tex](a-12)=0[/tex] and [tex](a+2)=0[/tex]

i.e. a= 12 and a= -2

Hence, the solutions of the given equation are,

[tex]a_{1}= 12[/tex] and [tex]a_{2}= -2[/tex].

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