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

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Question 172883: Solve by completing the square.
x² = 5x + 2
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(28504) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2=5x+%2B+2 Start with the given equation.


x%5E2-5x+=+2 Subtract 5x from both sides.


Take half of the x coefficient 5 to get 5%2F2. Square that value to get 25%2F4

x%5E2-5x+%2B25%2F4=+2%2B25%2F4 Add 25%2F4 to both sides.


x%5E2-5x+%2B25%2F4=+33%2F4 Combine like terms.


%28x-5%2F2%29%5E2+=33%2F4 Factor x%5E2-5x+%2B25%2F4 to get %28x-5%2F2%29%5E2


x-5%2F2=0%2B-sqrt%2833%2F4%29 Take the square root of both sides.


x-5%2F2=sqrt%2833%2F4%29 or x-5%2F2=-sqrt%2833%2F4%29 Break up the "plus/minus" to form two equations.


x-5%2F2=sqrt%2833%29%2F2 or x-5%2F2=-sqrt%2833%29%2F2 Simplify the square root.


x=5%2F2%2Bsqrt%2833%29%2F2 or x=5%2F2-sqrt%2833%29%2F2 Add 5%2F2 to both sides.


x=%285%2Bsqrt%2833%29%29%2F%282%29 or x=%285-sqrt%2833%29%29%2F%282%29 Combine the fractions.


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Answer:


So the solutions are x=%285%2Bsqrt%2833%29%29%2F%282%29 or x=%285-sqrt%2833%29%29%2F%282%29.

Answer by solver91311(16868) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Arrange your equation so that the variables are on the left and the constant term is on the right:

x%5E2=5x%2B2 => x%5E2-5x=2

Step 2: Divide both sides by the coefficient on the 2nd order term. In this case the coefficient is 1, so you can ignore this step.

Step 3: Divide the coefficient on the 1st order term by 2 and then square the result.

%285%2F2%29%5E2=25%2F4

Step 4: Add the result of Step 3 to both sides of the equation

x%5E2%2B5x%2B%2825%2F4%29=2%2B%2825%2F4%29

Step 5: You have now created a perfect square trinomial on the left. Factor it

%28x%2B%285%2F2%29%29%5E2=33%2F4

Step 6: Take the square root of both sides remembering to consider both the positive and negative roots

x%2B%285%2F2%29=sqrt%2833%2F4%29 or x%2B%285%2F2%29=-sqrt%2833%2F4%29

x%5B1%5D=%28-5%2Bsqrt%2833%29%29%2F2 or x%5B2%5D=%28-5-sqrt%2833%29%29%2F2

Those are the exact answers. You can use a calculator if you need numerical approximations