Solve by Completing the Square x^2+3x-1=0

Problem

x2+3*x−1=0

Solution

1. Isolate the constant term by adding 1 to both sides of the equation.

x2+3*x=1

2. Calculate the value needed to complete the square by taking half of the coefficient of x and squaring it: (3/2)2=9/4

Value=9/4

3. Add this value to both sides of the equation to maintain equality.

x2+3*x+9/4=1+9/4

4. Factor the left side as a perfect square trinomial and simplify the right side.

(x+3/2)2=13/4

5. Take the square root of both sides, remembering to include both the positive and negative roots.

x+3/2=±√(,13/4)

6. Simplify the radical on the right side.

x+3/2=±√(,13)/2

7. Solve for x by subtracting 3/2 from both sides.

x=−3/2±√(,13)/2

Final Answer

x=(−3±√(,13))/2

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