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Ans:

Guide: Product of Binomial⇒ (a+b)^2 = a^2+2ab+b^2

2x^2+9x+10=0 ⇒It is easy to complete the square of an equation if the numerical coefficient of the 1st term is 1. So divide both sides by 2.

x^2+(9/2)x+5=0 ⇒ transpose 5 to the right side so it will become -5.

x^2+(9/2)x=-5 ⇒from the left side of this equation we can use the guide above. So our value of a=1 set aside the variable, when we square the 1 the ans. is always 1. Let's come to (2ab): Our value of 2ab= (9/2) since we already have the value of a as 1 divide (9/2) by 2 to eliminate 2 in 2ab and we can find the value of b.

Our b=(9/4)

x^2+(9/2)x+(9/4)^2 = -5+(9/4)^2 ⇒we add both sides of the equation by b^2.

b=(9/4)

x^2+(9/2)x+(9/4)^2 = -5+(81/16)

[x+(9/4)]^2 = (1/16) ⇒use the guide: the left side. And square both sides of the equation to eliminate the squared of the left side.

x+(9/4)=√(1/16)

x+(9/4)=+ and - of (1/4) ⇒the square root of 1/16 is the positive and negative 1/4

x=+ and - (1/4)-(9/4)

or

x= +(1/4)-(9/4)=-2

x= -(1/4)-(9/4)=-5/2

To check: Use the Quadratic Formula