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# Solve x^{2} + 6x = 7 by completing the square. What is the solution set of the equation?

**Solution:**

Given equation x^{2} +6x = 7

Using the method of completing the square, let us find the solution set that satisfies the equation.

- Divide the coefficient of the x term by 2 then square the result.
- This number will be added to both sides of the equation.

Step 1: Rearrange the equation in the form of ax^{2 }+ bx = c, if necessary.

⇒ x^{2} + 6x = 7

Step 2: Add (b/ 2)^{2} on both the sides of the equation, b = 6 (coefficient of x)

⇒ x^{2} + 6x + (6/ 2)^{2 }= 7 + (6/ 2)^{2}

Step 3: Factorize the sides using algebraic identity (a + b)^{2 }into perfect squares.

⇒ (x + 3 )^{2} = 7 + (3)^{2}

Step 4: Take square root on both the sides.

⇒ √ (x + 3 )^{2} = √ 16

Step 5: Solve for x.

⇒ x + 3 = ± 4

⇒ x = ± 4 - 3

⇒ x = - 7 or 1

Thus the solution set is {-7,1}

## Solve x^{2} + 6x = 7 by completing the square. What is the solution set of the equation?

**Summary:**

By solving x^{2 }+ 6x = 7 by completing the square, we get thea solution set as {-7, 1}.

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