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What number must you add to complete the square? x^2+26x=33

Sagot :

sreedevi102

Answer:

Must add: 202

Step-by-step explanation:

[tex]The \ formula \ for \ perfect \ square => (a + b)^2 = a^2 + 2ab + b^2[/tex]

a = x

2ab = 26x

2ab = 26a  [ substitute a instead of x]

[tex]b = \frac{26a}{2a}[/tex]

b= 13

So,

  [tex](x + 13)^2 = x^2 + 26x + 169[/tex]

But given equation is :

       [tex]x^2 + 26x = 33\ => \ x^2 + 26x -33 = 0[/tex]

We have find the difference between 169 and -33 to get the number that should be added to get the perfect square.

That is , 169 - (-33) = 202

Therefore ,

   [tex]x^2 + 26x -33 + 202 \ makes \ given \ equation \ a \ perfect \ square[/tex]

MisterBrainly
  • x²+26x=33

Multiply by 4a

  • 4x²+104x=132
  • (2x)²+2(2x)(21)=132

21²=441 must be added to get complete square

Remark

You can also add 13² =169 as 2(13)(x)=26x

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