SOLUTION: It asks to solve by completing the square, the problem is: x^2-6x=16 Please and Thank You=)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: It asks to solve by completing the square, the problem is: x^2-6x=16 Please and Thank You=)       Log On


   

Question 131145: It asks to solve by completing the square, the problem is: x^2-6x=16
Please and Thank You=)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x=16
in standard form:
x%5E2-6x-16=0

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form


y=1+x%5E2-6+x-16 Start with the given equation



y%2B16=1+x%5E2-6+x Add 16 to both sides



y%2B16=1%28x%5E2-6x%29 Factor out the leading coefficient 1



Take half of the x coefficient -6 to get -3 (ie %281%2F2%29%28-6%29=-3).


Now square -3 to get 9 (ie %28-3%29%5E2=%28-3%29%28-3%29=9)





y%2B16=1%28x%5E2-6x%2B9-9%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 9 does not change the equation




y%2B16=1%28%28x-3%29%5E2-9%29 Now factor x%5E2-6x%2B9 to get %28x-3%29%5E2



y%2B16=1%28x-3%29%5E2-1%289%29 Distribute



y%2B16=1%28x-3%29%5E2-9 Multiply



y=1%28x-3%29%5E2-9-16 Now add %2B16 to both sides to isolate y



y=1%28x-3%29%5E2-25 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=3, and k=-25. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=1x%5E2-6x-16 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2-6x-16%29 Graph of y=1x%5E2-6x-16. Notice how the vertex is (3,-25).



Notice if we graph the final equation y=1%28x-3%29%5E2-25 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x-3%29%5E2-25%29 Graph of y=1%28x-3%29%5E2-25. Notice how the vertex is also (3,-25).



So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.