Step-by-step explanation:
a) There's a mistake at the third step from the beginning.
b) Instead of adding 25 , Josh added 100. While solving an equation using "Completing Squares Method" , we need to write the L.H.S. in the form of [tex]a^{2} + 2ab + b^{2}[/tex] or [tex]a^{2} - 2ab + b^{2}[/tex] , so that in the next step it can be converted into [tex](a + b)^{2}[/tex] or [tex](a - b)^{2}[/tex].
c) [tex]x^{2} + 10x - 88 = 8[/tex]
Taking -88 to R.H.S. , it's sign changes and becomes +88.
[tex]=> x^2 + 10x = 88 + 8 = 96[/tex]
Using "Completing Squares Method" , L.H.S. can be written as :-
[tex](x)^{2} + 2 \times x \times 5 + (5)^{2} = 96 + (5)^{2}[/tex]
[tex]=> (x + 5)^{2} = 96 + 25 = 121[/tex]
[tex]=> x + 5 = \sqrt{121} = -11 \: or +11[/tex]
[tex]=> x = +6 \: or -16[/tex]
