Q:

Solve the quadratic equation. 8x^2 + 16x + 8 = 0

Accepted Solution

A:
Hello there!

We will solve this by completing the square.

The solutions are: 

x₁ = −1 

x₂ = −1
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 Explanation:

STEP 1: Divide equation by whatever is multiplied on the squared term. In this case we will divide with 8. x^2 + 2x + 1 = 0
 

STEP 2: Keep all terms containing x on one side. Move the constant to the right. x^2 + 2x = −1


 STEP 3: Take half of the x-term coefficient and square it. Add this value to both sides. 

In this example we have: 

The x-term coefficient = 2

The half of the x-term coefficient = 1 

After squaring we have 12 = 1 

When we add 1 to both sides we have: 

x^2 + 2x + 1 = −1 + 1 


STEP 4: Simplify right side x^2 + 2x + 1 = 0 


STEP 5: Write the perfect square on the left. (x + 1)2 = 0 


STEP 6: Take the square root of both sides. x + 1 = ± √ 0 


STEP 7: Solve for x. x = −1 ± √ 0 

That is x₁ = −1 and x₂ = −1



I hope I helped!

Let me know if you need anything else!

~ Zoe