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

Problem

x2+14*x+4=0

Solution

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

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=7

7=49

3. Add the calculated value 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=45

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

√(,(x+7)2)=±√(,45)

x+7=±3√(,5)

6. Isolate the variable x by subtracting 7 from both sides.

x=−7±3√(,5)

Final Answer

x=−7±3√(,5)

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