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3 years ago

Rewrite the equation by completing the squares x^2-x-20

Mathematics

1 answer:

yuradex [85]3 years ago

3 0

Answer: x = ¹/₂ ± √⁸¹

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Step-by-step explanation:

First write out the equation

x² - x - 20

Now we now write the equation by equating to 0

x² - x - 20 = 0

We now move 20 to the other side of the equation. So

x² - x = 20,

We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes

x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²

x² - ( ¹/₂ )² = 20 + ¹/₄

( x - ¹/₂ )² = 20 + ¹/₄, we now resolve the right hand side expression into fraction

( x - ¹/₂ )² = ⁸¹/₄ when the LCM is made 4

Taking the square root of both side to remove the square,we now have

x - ¹/₂ = √⁸¹/₄

x - ¹/₂ = √⁸¹/₂

Therefore,

x = ¹/₂ ± √⁸¹

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