Solve by Completing the Square x^2+10x+13=0

Problem

x2+10*x+13=0

Solution

1. Isolate the constant term by subtracting 13 from both sides of the equation.

x2+10*x=−13

2. Calculate the value needed to complete the square by taking half of the coefficient of x and squaring it: (10/2)2=5=25

(10/2)2=25

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

x2+10*x+25=−13+25

4. Factor the left side into a perfect square binomial and simplify the right side.

(x+5)2=12

5. Apply the square root property to both sides, remembering to include the plus-minus sign.

x+5=±√(,12)

6. Simplify the radical √(,12) as √(,4⋅3)=2√(,3)

x+5=±2√(,3)

7. Solve for x by subtracting 5 from both sides.

x=−5±2√(,3)

Final Answer

x=−5±2√(,3)

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