Problem

Solve the equation by completing the square: \(x^2 - 6x + 5 = 0\)

Answer

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Answer

Finally, we take the square root of both sides and solve for \(x\), obtaining two possible solutions: \(x = 3 + 2\) or \(x = 3 - 2\)

Steps

Step 1 ：First, we rearrange the equation to form a perfect square trinomial on the left side. So, we have \(x^2 - 6x = -5\)

Step 2 ：Next, we add the square of half the coefficient of \(x\), which is \((-6/2)^2 = 9\), to both sides to complete the square. This gives us \((x^2 - 6x + 9) = -5 + 9\)

Step 3 ：The left side of the equation now factors as a perfect square, \((x - 3)^2 = 4\)

Step 4 ：Finally, we take the square root of both sides and solve for \(x\), obtaining two possible solutions: \(x = 3 + 2\) or \(x = 3 - 2\)

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