Hi  

Solve this quadratic equation by completing the square and rounding the solution to nearest hundredth.



x^2 - 10x + 25 - 25 + 10 = 0

(x-5)^2 -15 = 0

(x-5)^2 = 15    |Taking the square root of both sides

 x-5 = ± √15   

x = 5  ± √15     √15 =3.87

x = 8.87  0r x = 1.13

Wish You the Best in your Studies.

 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 start with:

x^2 - 10x + 10 = 0





subtract 10 from both sides of the equation to get:

x^2 - 10x = -10





take half the coefficient of the x term and adding it to x to get (x - 5)^2 = -10

(x - 5)^2 is equal to x^2 -10x + 25

to make (x - 5)^2 equal to x^2 - 10x, you need to subtract 25 from the result.

you get (x - 5)^2 - 25 = -10

add 25 to both sides of the equation to get:

(x - 5)^2 = 15





take the square root of both sides of this equation to get:

x - 5 = plus or minus sqrt(15)

add 5 to both sides of this equation to get:

x = 5 plus or minus sqrt(15)

that's your solution.



if you graph the equations of x^2 - 10x + 10 = y, and (x - 5)^2 - 15 = y, they should be identical.





the following graph shows that they are:











the roots shown are 1.127 and 8.873.

5 + sqrt(15) = 8.873 rounded to 3 decimal places.

5 - sqrt(15) = 1.127 rounded to 3 decimal places.





both equations draw the same graph.

this means they are identical.

they are two different versions of the same equation.





your solution is x = 5 plus or minus sqrt(15)





 

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