Solve by Completing the Square x^2-10x-4=0

Problem

x2−10*x−4=0

Solution

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

x2−10*x=4

2. Calculate the value needed to complete the square by taking half of the coefficient of x which is −10 and squaring it.

((−10)/2)2=(−5)2=25

3. Add 25 to both sides of the equation to maintain equality.

x2−10*x+25=4+25

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

(x−5)2=29

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

x−5=±√(,29)

6. Solve for x by adding 5 to both sides.

x=5±√(,29)

Final Answer

x=5±√(,29)

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