Question

Solve the quadratic equation for 'x' and give your answer to three significant figures -:

2x (x-2) - 3 = 0

Show each & every step !!

Answer 1

Hope u like my process
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=> A quadratic equation can be solved in many ways..

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Few steps are.
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$= > 2x(x - 2) - 3 = 0 \\ \\ = > 2 {x}^{2} - 4x - 3 = 0 \\ \\ = > {x}^{2} - 2x - \frac{3}{2} = 0..(dividing \: \: 2 \: \: on \: \: both \: \: sides) \\ \\ = > {x}^{2} - 2x + 1 = \frac{3}{2} + 1..(adding \: \: 1 \: \: on \: \: both \: \: sides) \\ \\ = > {(x - 1)}^{2} = \frac{5}{2} \\ \\ = > {(x - 1)} = \sqrt{ \frac{5}{2} } \\ \\ \bf \underline{either} \\ \\ = >x = 1 + \sqrt{ \frac{5}{2} } \\ \\ \bf \: \underline{or} \\ \\ = > x = 1 - \sqrt{ \frac{5}{2} }$
Even it can be taken out by shreedhar acharyas Formula.

$= > x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ = > x = \frac{ - (- 2 )+ - \sqrt{4 - 4 \times 1 \times ( - \frac{3}2}) }{2} \\ \\ = > x = \frac{ 2 + - \sqrt{4 + 6} }{2} = \frac{ 2 + - \sqrt{10} }{2} \\ \\ thus \: ..either \\ \\ = > x = 1 - \sqrt{ \frac{5}{2} } ....or.... 1 + \sqrt{ \frac{5}{2} }$

Thus the required answer is

$= > \boxed{ \bf \: x = \underline{ \orange{(1 - \sqrt\frac{5}{2}) } \: \: \: \: or \: \: \orange{(1 + \sqrt{ \frac{5}{2} }) }} }$

So the value of x can be

Either
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=>x = 1 - 1.581 = 0.581

Or
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=> x = 1 + 1.581 = 2.581
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Hope this is ur required answer

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