Solve by Completing the Square x^2-4x+3=0

Problem

x2−4*x+3=0

Solution

1. Isolate the constant term by subtracting 3 from both sides of the equation.

x2−4*x=−3

2. Calculate the value needed to complete the square by taking half of the coefficient of x which is −4 and squaring it.

((−4)/2)2=(−2)2=4

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

x2−4*x+4=−3+4

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

(x−2)2=1

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

x−2=±√(,1)

x−2=±1

6. Solve for x by adding 2 to both sides for both cases.

x=2+1⇒x=3

x=2−1⇒x=1

Final Answer

x=3,1

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