Solve by Completing the Square (x^2)/2+5/2x=2

Problem

(x2)/2+5/2*x=2

Solution

1. Multiply by 2 to clear the denominators and ensure the leading coefficient of x2 is 1.

2⋅((x2)/2+5/2*x)=2⋅2

x2+5*x=4

2. Identify the constant needed to complete the square by taking half of the coefficient of x and squaring it.

(5/2)2=25/4

3. Add the constant to both sides of the equation.

x2+5*x+25/4=4+25/4

4. Simplify the right side by finding a common denominator.

4+25/4=16/4+25/4

x2+5*x+25/4=41/4

5. Factor the left side as a perfect square trinomial.

(x+5/2)2=41/4

6. Take the square root of both sides, remembering to include the plus-minus sign.

x+5/2=±√(,41/4)

x+5/2=±√(,41)/2

7. Isolate x by subtracting 5/2 from both sides.

x=−5/2±√(,41)/2

x=(−5±√(,41))/2

Final Answer

(x2)/2+5/2*x=2⇒x=(−5±√(,41))/2

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