Verified answer

Completing the Square

1. x² + 4x = -3

• x² + 4x + 4 = -3 + 4
• √(x + 2)² = √1
• x + 2 = ± 1
• x + 2 = 1, x = -1
• x + 2 = -1, x = -3

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2. 2x² + 8x = 4

• x² + 4x = 2
• x² + 4x + 4 = 2 + 4
• (x + 2)² = 6
• x + 2 = ±6
• x = -2±√6

Steps in completing the square:

1. Write the quadratic equation in the form ax² + bx = c.
2. Add (b/2)² on both sides of the equation to make the left side of the equation a perfect square trinomial.
3. Factor the perfect square trinomial on one side and simplify another one.
4. Apply the square root property to solve for x.

Answer:

• 1. x = -1, -3
• 2. x = -2±√6