Answer: x = ¹/₂ ± √⁸¹
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2
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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2
Answer:
x^2 - 8xy + 3y^2 - 2
Step-by-step explanation:
(-8xy + 2x^2 + 3y^2) - unknown = x^2 + 2
- unknown = x^2 + 2 + 8xy - 2x^2 - 3y^2
- unknown = -x^2 + 8xy - 3y^2 + 2
Unknown = x^2 - 8xy + 3y^2 - 2
Check:
(-8xy + 2x^2 + 3y^2) - (x^2 - 8xy + 3y^2 - 2)
= -8xy + 2x^2 + 3y^2 - x^2 + 8xy - 3y^2 + 2
= -8xy + 8xy + 2x^2 - x^2 + 3y^2 - 3y^2 + 2
= x^2 + 2
Answer:
2k
Step-by-step explanation:
3k and -k are both like terms, so you can combine them. Adding opposite signs works in the same way as subtraction, so you can rewrite the expression as 3k-k, which is 2k.
