2x+2x+4=0 solve it fast plzzz
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Answer:
Hey mate here is ur answer mark it as brainliest
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Given & To find:
Solve for x using completing the square method,.
2x² + x - 4 = 0,
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As, we know that,
(a + b)² = a² + 2ab + b²
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We are intended to find the value of x, using this formula,.
=> For doing that, we need to bring this equation to that form (a² + 2ab + b² for some value a & b.,.)
We take an attempt to bring this equation to that form,
=> 2x² + x - 4 = 0,
=> x^2 + \frac{x}{2} - 2 = 0 (Dividing both the sides by \frac{1}{2} ),
=> x^2 + 2( \frac{1}{4} ) x - 2 = 0
(Multiplying & dividing the middle term by 2 to get the term 2ab (here a = x, b = \frac{1}{2} ))
So, we have the form,
a² + 2ab + c (for some value c, here it is - 4), we need b² to bring this equation to that form,
By adding ( \frac{1}{4}) ^2 both the sides ,
we get,
=> x^2 + 2\frac{1}{4}x + ( \frac{1}{4} ) ^2 - 2 = ( \frac{1}{4} )^2
It can be, reduced to the form (a + b)²
=> (x + \frac{1}{4} )^2 - 2 = \frac{1}{16}
=> (x + \frac{1}{4} )^2 = \frac{1}{16} + 2
=> (x + \frac{1}{4} )^2 = \frac{1+32}{16}
=> (x + \frac{1}{4} )^2 = \frac{33}{16}
By moving the square from LHS to RHS, we get,
=> (x + \frac{1}{4} ) = \sqrt{ \frac{33}{16} }
=> (x + \frac{1}{4} ) = \frac{ \sqrt{33} }{4} (or) (x + \frac{1}{4} ) = \frac{ - \sqrt{33} }{4}
=> x = \frac{ \sqrt{33} }{4} - \frac{1}{4} (or) x = \frac{ - \sqrt{33} }{4} - \frac{1}{4}
=> x = \frac{ \sqrt{33} - 1 }{4} (or) x = \frac{ -\sqrt{33} - 1}{4}
It's completed,.
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Hope it Helps !!
=> Mark as Brainliest,..
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