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# Solve x^{2} - 8x = 3 by completing the square. Which is the solution set of the equation?

**Solution:**

Given equation x^{2} - 8x = 3

For completing the square we follow these steps:

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

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} – 8 x = 3

Step 2: Add (b/2)^{2} on both the sides of the equation, b = - 8 (coefficient of x)

⇒ x^{2} - 8x + (- 8 / 2)^{2 }= 3 + ( - 8 / 2)^{2}

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

⇒ ( x - 8 / 2 )^{2} = 3 + ( - 4 )^{2}

Step 4: Square root on both the sides.

⇒ √ (x - 8/ 2 )^{2} = √19

Step 5: Solve for x.

⇒ x - 4 = ± √ 19

⇒ x = ± √ 19 + 4

⇒ x = 4 + √ 19 or 4 - √ 19

The solution set is {4 + √ 19 ,4 - √ 19}

## Solve x^{2} - 8x = 3 by completing the square. Which is the solution set of the equation?

**Summary:**

By solving x^{2} - 8x = 3 by completing the square, the solution set is {4 + √ 19 ,4 - √ 19}

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