Solve by Completing the Square x^2+10x+7=0

Problem

x2+10*x+7=0

Solution

1. Isolate the constant term by subtracting 7 from both sides of the equation.

x2+10*x=−7

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

10/2=5

5=25

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

x2+10*x+25=−7+25

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

(x+5)2=18

5. Take the square root of both sides, remembering to include the plus-minus sign.

√(,(x+5)2)=±√(,18)

x+5=±3√(,2)

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

x=−5±3√(,2)

Final Answer

x=−5±3√(,2)

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