Question

2x²+x-4=0 solve it by completing square method. ​

Answer 1

hello mate ❤

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Answers

Solution:

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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

=> 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\x + ) ^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}

It's completed,.

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☺✌I hope its help u ❤