Question

Solve for a.

25=a2+b2



A: a=5−b or a=5+b

B: a=25−b^2
C: a=±25−b^2−−−−−−√
d: a=±25+b2−−−−−−√

Answer 1

The correct answer is:  [C]:  " a =  ± $\sqrt{25 - b^2}$  " .
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Explanation:
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We are given:  
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    →   "  25  =  a²  +  b²  "  ;   Solve for "a" ; 
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    →  To solve for "a" ;  we want to isolate "a" on one side of the equation.
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We can rewrite:  "  25  =  a²  +  b²  "  ;

as:  " a²  +  b²  = 25 " .

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Then, we can subtract " b² "  from each side of the equation; as follows:
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   →  " a²  +  b²  −  b²  =  25 − b²  "  ;

to get:
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   →  " a²  =  25 − b²  "  ;
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  →  Now,  take the square root of EACH SIDE of the equation ; 
to isolate "a" on one side of the equation; & to solve for the value(s) of "a" ; 
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  →  √(a²)  = $\sqrt{25 - b^2}$  ;

to get:
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  →    a   =  | $\sqrt{25 - b^2}$ |  ;

  →    a   =  ±  $\sqrt{25 - b^2}$  ; 
  
  →  which is:  Answer choice:  [C]:  " a =  ±  $\sqrt{25 - b^2}$  " .
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