Solve x² + 8x = 33 by completing the square. Which is the solution set of the equation?
{-11, 3}, {-3, 11}, {-4, 4}, {-7, 7}

Solution:

Given equation x² + 8x = 33

We complete the square for making the LHS into a perfect square trinomial.

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

For the quadratic equation x² - 8x = 3, the coefficient of the x term is 8

So (8/2)² = (4)² = 16

⇒ x² + 8x +16 = 33 + 16

⇒ x² + 2(4)(x) + 16 = 49

⇒ {x² + 2(x)(4) + 4²} = 49 [ since a² + 2ab + b² = (a + b)²]

⇒ (x + 4)² = 49

Applying square root on both sides, we get

⇒ x + 4 = √49

⇒x = ±7 - 4

⇒ x  = -11, 3

The solution set is {-11, 3}

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Solve x² + 8x = 33 by completing the square. Which is the solution set of the equation?

Summary:

By solving the equation x² + 8x = 33 by completing the square, we get solution set as {-11, 3}.