The given equation is: [tex] 4x^{2} [/tex]+8x-7=0
We will solve using completing the square:
On dividing both the sides by 4 , we get,
[tex] x^{2} + \frac{8x}{4} - \frac{7}{4} [/tex] =0
Now, adding 1 to both sides we get,
[tex] x^{2} + \frac{8x}{4} - \frac{7}{4} [/tex] + 1 = 1
On rearranging the terms we get,
[tex] (x^{2} + 2x + 1) = 1 + \frac{7}{4} [/tex]
[tex] (x + 1)^{2} [/tex] = 1 +[tex] \frac{7}{4} [/tex]
[tex] (x+1 )^{2} = \frac{11}{4} [/tex]
On taking sqaure root we get,
[tex](x + 1) = + \frac{ \sqrt{11} }{2} ; - \frac{ \sqrt{11} }{2} [/tex]
Therefore, [tex]x = \frac{ \sqrt{11} }{2} -1
[/tex][tex]x = - \frac{ \sqrt{11} }{2} -1 [/tex]
