SOLUTION: Hello, I am stuck on this one. This is college algebra. I am suppose to complete the square. x squared + 7x -4 =0

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Question 487237: Hello, I am stuck on this one. This is college algebra. I am suppose to complete the square.
x squared + 7x -4 =0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2+%2B+7x+-4+=0

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


y=1+x%5E2%2B7+x-4 Start with the given equation



y%2B4=1+x%5E2%2B7+x Add 4 to both sides



y%2B4=1%28x%5E2%2B7x%29 Factor out the leading coefficient 1



Take half of the x coefficient 7 to get 7%2F2 (ie %281%2F2%29%287%29=7%2F2).


Now square 7%2F2 to get 49%2F4 (ie %287%2F2%29%5E2=%287%2F2%29%287%2F2%29=49%2F4)





y%2B4=1%28x%5E2%2B7x%2B49%2F4-49%2F4%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 49%2F4 does not change the equation




y%2B4=1%28%28x%2B7%2F2%29%5E2-49%2F4%29 Now factor x%5E2%2B7x%2B49%2F4 to get %28x%2B7%2F2%29%5E2



y%2B4=1%28x%2B7%2F2%29%5E2-1%2849%2F4%29 Distribute



y%2B4=1%28x%2B7%2F2%29%5E2-49%2F4 Multiply



y=1%28x%2B7%2F2%29%5E2-49%2F4-4 Now add %2B4 to both sides to isolate y



y=1%28x%2B7%2F2%29%5E2-65%2F4 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=-7%2F2, and k=-65%2F4. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=1x%5E2%2B7x-4 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2%2B7x-4%29 Graph of y=1x%5E2%2B7x-4. Notice how the vertex is (-7%2F2,-65%2F4).



Notice if we graph the final equation y=1%28x%2B7%2F2%29%5E2-65%2F4 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x%2B7%2F2%29%5E2-65%2F4%29 Graph of y=1%28x%2B7%2F2%29%5E2-65%2F4. Notice how the vertex is also (-7%2F2,-65%2F4).



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