Solve x² - 8x = 3 by completing the square. Which is the solution set of the equation?

Solution:

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

⇒ x² – 8 x = 3

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

⇒ x² - 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}

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Solve x² - 8x = 3 by completing the square. Which is the solution set of the equation?

Summary:

By solving x² - 8x = 3 by completing the square, the solution set is {4 + √ 19 ,4 - √ 19}