Solve by Completing the Square x^2+10x+14=0

Problem

x2+10*x+14=0

Solution

1. Isolate the constant term by subtracting 14 from both sides of the equation.

x2+10*x=−14

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=25

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

x2+10*x+25=−14+25

4. Simplify the right side and write the left side as a perfect square trinomial.

(x+5)2=11

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

x+5=±√(,11)

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

x=−5±√(,11)

Final Answer

x=−5±√(,11)

Want more problems? Check here!