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

A quadratic equation is in the form of ax^{2 }+ bx + c = 0. To find the roots of the quadratic equation, we can use completing the square method.

## Answer: The set of solutions for the equation x^{2} + 6x = 7 is - 7 or 1 by completing the squares.

Let's find the solution set that satisfies the equation.

**Explanation:**

Let's find the solution step by step.

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

⇒ (x + 6/ 2 )^{2} = 7 + (3)^{2}

Step 4: Square root on both the sides.

⇒ √ (x + 6/ 2 )^{2} = √ 16

Step 5: Solve for x.

⇒ x + 3 = ± 4

⇒ x = ± 4 - 3

⇒ x = - 7 or 1

We can solve the quadratic equation using Cuemath's online quadratic equation calculator.