Question

B. x2 - 16x + 64 = 20

Answer 1

Answer:

$x_1 = 8+2\sqrt{5}=2(4+\sqrt{5} )$

$x_2 = 8-2\sqrt{5}=2(4-\sqrt{5} )$

Step-by-step explanation:

$x^2 - 16x + 64 = 20$

I will solve it completing the square

$x^2 - 16x + 64 = 20$

$(x-8)^2 = 20$

$x-8= \pm\sqrt{20}$

$x=8 \pm\sqrt{20}$

$x=8 \pm2\sqrt{5}$

$x_1 = 8+2\sqrt{5}=2(4+\sqrt{5} )$

$x_2 = 8-2\sqrt{5}=2(4-\sqrt{5} )$

Answer 2

Answer:  The answer is:  " x  =  8  ±  2√5  " .

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Step-by-step explanation:

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Given:

  x² - 16x + 64 = 20 ;  Solve for "x" ;

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Subtract "20" from each side of the equation:

  x² - 16x + 64 - 20 = 20 -20 ;

to get:

  x² - 16x + 44 = 0  ;

(i.e. to get an equation in "quadratic equation format" ;

that is; in the format of:    ax² + bx + c = 0 ;  (a ≠ 0) ;

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We cannot factor the "left-hand side" of the equation;

so, we can solve for "x" by using the quadratic equation formula;

Note that our equation:  " x² - 16x + 44 = 0 " ;

              is in "quadratic equation format" ;

    that is:  " ax² + bx + c = 0 " ;  (a ≠ 0) ;

                in which:

                   a  =  1 ;

(Note:  The implied coefficient of:  " ax² "  is:   "1" ;

     →  since "1" ; multiplied by any value, results in that exact value.

 This is known as the "identity property" of multiplication.}.

                   b  =  -16 ;

                   c  =  44  .

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To solve for "x" ; we use the quadratic equation formula:

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         →   x  =  [ - b  ± √(b² - 4ac) ]  /  [2a] ;

We solve for "x" by plugging in our values for "a" ; "b" ; and "c" ;

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         →   x  =  { - [-16) ± {√[(-16)² - 4(1)(44) ] }   /  [2 * 1]  ;

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        →    x  =  [ 16  ±  √ (16² - 4*44) ]  / [2] ;

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        →    x  =  [ 16  ±  √ (16² - 4*44) ]  / [2] ;

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        →    x  =  [ 16  ±  √ (256 - 176 )]  / [2] ;

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        →    x  =  [ 16  ±  √ (80 )]  / [2] ;

Now, let us rewrite:  " √80 " ;

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  " √80 " =  √16 * √5  =  4*√5 ;

                                     →  write as:  " 4√5 " .

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Now, take:

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        →    x  =  [ 16  ±  √ (80 )]  / [2] ;

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And replace:  " √80 " ;   with:   " 4√5 " ;  and rewrite:

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        →    x  =  [ 16  ±  4√5 )  / 2 ;

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Now, divide the numerator by "2" to simplify, and rewrite:

       →  Note:  16 ÷ 2 = 8 ; and:  4 ÷ 2 = 2 ;

So, we have:

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        →    x  =  8  ±  2√5

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