Solve by Completing the Square x^2+6x=7

Problem

x2+6*x=7

Solution

1. Identify the coefficient of the linear term x which is 6

2. Calculate the value needed to complete the square by taking half of the linear coefficient and squaring it: (6/2)2=3=9

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

x2+6*x+9=7+9

4. Simplify the right side of the equation.

x2+6*x+9=16

5. Factor the left side as a perfect square trinomial.

(x+3)2=16

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

x+3=±√(,16)

x+3=±4

7. Solve for x by subtracting 3 from both sides, resulting in two separate equations.

x=−3+4⇒x=1

x=−3−4⇒x=−7

Final Answer

x=1,−7

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