Question

slove the following quadratic equations by completing square method 2x+6x-7=0​

Answer 1

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Answer 2

$2 {x}^{2} + 6x - 7 = 0 \\ \\ \frac{2}{2} {x}^{2} + \frac{6}{2} x - \frac{7}{2} = \frac{0}{2} \\ \\ {x}^{2} + 3x = \frac{7}{2} \\ \\ {x}^{2} + 2 \times x \times \frac{3}{2} + { \left( \frac{3}{2} \right)}^{2} = \frac{7}{2} + { \left( \frac{3}{2} \right)}^{2} \\ \\ { \left( x \: + \frac{3}{2} \right)}^{2} = \frac{23}{4} \\ \\ x + \frac{3}{2} = \pm \frac{ \sqrt{23} }{2}$

Case 1

$x + \frac{3}{2} = \frac{ \sqrt{23} }{2} \\ \\ x = \frac{ \sqrt{23} }{2} - \frac{3}{2} \\ \\ x = \frac{ \sqrt{23} - 3}{2}$

Case 2

$x + \frac{3}{2} = - \frac{ \sqrt{23} }{2} \\ \\ x = - \frac{ \sqrt{23} }{2} - \frac{3}{2} \\ \\ x = \frac{ - \sqrt{23} - 3 }{2} \\ \\ x = - \frac{ \sqrt{23} + 3}{2}$