Solve x² + 6x = 7 by completing the square. What is the solution set of the equation?

Solution:

Given equation x² +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 ax² + bx = c, if necessary.

⇒ x² + 6x = 7

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

⇒ x² + 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}

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Solve x² + 6x = 7 by completing the square. What is the solution set of the equation?

Summary:

By solving x² + 6x = 7 by completing the square, we get thea solution set as {-7, 1}.