Find the solutions of each quadratic equation by completing the square
1. [tex]x^{2} + 6x - 16 = 0[/tex]
2. [tex]x^{2} + 7x - 4 = 0[/tex]
3. [tex]x^{2} - 14x - 100 = 0[/tex]
Answer (1)
x = 2, x = -82. x² + 7x - 4 = 0Step 1: Move the constantx² + 7x = 4Step 2: Complete the squareHalf of 7 is 7/2 → (7/2)² = 49/4Add 49/4 to both sides:x² + 7x + 49/4 = 4 + 49/4Convert 4 to 16/4 → 16/4 + 49/4 = 65/4Now: (x + 7/2)² = 65/4Step 3: Solve by square rootx + 7/2 = ±√(65/4) → x + 7/2 = ±√65 / 2Step 4: Solve for xx = -7/2 ± √65 / 2
