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