Question

Use the completing the square method to find the roots of 2x^2+3x-15=13 include the steps, it would be greatly appreciated thanks!!

Answer 1

The roots are

`x1= (-3+√(233))/(4)`

`x2= (-3-√(233))/(4)`

Explanation:

we have

`2x^(2)+3x-15=13`

so

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`2x^(2)+3x=13+15`

`2x^(2)+3x=28`

Factor the leading coefficient

`2(x^(2)+(3/2)x)=28`

Complete the square. Remember to balance the equation by adding the same constants to each side

`2(x^(2)+(3/2)x+(9/16))=28+(9/8)`

`2(x^(2)+(3/2)x+(9/16))=233/8`

`(x^(2)+(3/2)x+(9/16))=233/16`

Rewrite as perfect squares

`(x+(3/4))^(2)=233/16`

square root both sides

`(x+(3)/(4))=(+/-)\sqrt{(233)/(16)}\\ \\(x+(3)/(4))=(+/-)(√(233))/(4)\\ \\x= -(3)/(4)(+/-)(√(233))/(4)`

`x1= -(3)/(4)(+)(√(233))/(4)=(-3+√(233))/(4)`

`x2= -(3)/(4)(-)(√(233))/(4)=(-3-√(233))/(4)`