Solve by Completing the Square x^2-18x-4=0

Problem

x2−18*x−4=0

Solution

1. Move the constant term to the right side of the equation by adding 4 to both sides.

x2−18*x=4

2. Find the value to complete the square by taking half of the coefficient of x which is −18 and squaring it.

(−18)/2=−9

(−9)2=81

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

x2−18*x+81=4+81

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

(x−9)2=85

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

√(,(x−9)2)=±√(,85)

x−9=±√(,85)

6. Isolate the variable by adding 9 to both sides.

x=9±√(,85)

Final Answer

x=9±√(,85)

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