SOLUTION: Solve by completing the square. x2 = 5x + 2

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Question 978593: Solve by completing the square. x2 = 5x + 2
Found 2 solutions by 428225, ikleyn:
Answer by 428225(90) About Me  (Show Source):
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!

1. Rewrite your equation as

x%5E2+-+5x+-+2 = 0.

2. Complete the square for the polynomial in the left side

x%5E2+-5x+-+2 = %28x-5%2F2%29%5E2 - %285%2F2%29%5E2 - 2 = %28x-5%2F2%29%5E2 - 25%2F4 - 2 = %28x-5%2F2%29%5E2 - %2825+%2B+2%2A4%29%2F4 = %28x-5%2F2%29%5E2 - 33%2F4.

3. Now your equation is

%28x-5%2F2%29%5E2 - 33%2F4 = 0.

4. Rewrite it in the form

%28x-5%2F2%29%5E2 = 33%2F4.

5. Take the square root in both sides:

x-5%2F2 = +/- sqrt%2833%29%2F2.

6. Now x = 5%2F2 +/- sqrt%2833%29%2F2.

You got two roots. Congratulations!