Solve by Completing the Square x^2-14x-4=0

Problem

x2−14*x−4=0

Solution

1. Isolate the constant term by adding 4 to both sides of the equation.

x2−14*x=4

2. Calculate the value needed to complete the square by taking half of the coefficient of x which is −14 and squaring it.

((−14)/2)2=(−7)2=49

3. Add 49 to both sides of the equation to maintain equality.

x2−14*x+49=4+49

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

(x−7)2=53

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

x−7=±√(,53)

6. Solve for x by adding 7 to both sides.

x=7±√(,53)

Final Answer

x=7±√(,53)

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