0
-2x^2 - 8x + 1 = 0
x^2 + 4x - 1/2 = 0
x^2 + 4x = 1/2
x^2 + 4x + 4 = 9/2
(x + 2)^2 = 9/2
x + 2 = ±√(9/2)
x = ±√[(9)(2)/(2)(2)] - 2
x = ±(3/2)√2 - 2
x = (3/2)√2 - 2 or x = -(3/2)√2 - 2
Check:
-2x^2 - 8x + 1 = 0
-2[(3/2)√2 - 2]^2 - 8[(3/2)√2 - 2] + 1 =? 0
-2(9/2 - 6√2 + 4) - 12√2 + 16 + 1 =? 0
-9 + 12√2 - 8 - 12√2 + 16 + 1 =? 0
-17 + 17 =? 0
0 = 0 True
-2x^2 - 8x + 1 = 0
-2[-(3/2)√2 - 2]^2 - 8[-(3/2)√2 - 2] + 1 =? 0
-2[-[(3/2)√2 + 2]]^2 - 8[-(3/2)√2 - 2] + 1 =? 0
-2(9/2 + 6√2 + 4) + 12√2 + 16 + 1 =? 0
-9 - 12√2 - 8 + 12√2 + 16 + 1 =? 0
-17 + 17 =? 0
0 = 0 True
To solve the quadratic equation y = -2x^2 - 8x + 1 by completing the square, follow these steps:
- Move the constant term (1) to the right side of the equation: y - 1 = -2x^2 - 8x.
- Divide the equation by the coefficient of x^2 (-2): (y - 1)/(-2) = x^2 + 4x.
- Complete the square by adding (4/2)^2 = 4 to both sides of the equation: (y - 1)/(-2) + 4 = x^2 + 4x + 4.
- Simplify: (y - 1)/(-2) + 4 = (x + 2)^2.
- Rewrite the equation in the vertex form: (y - 1)/(-2) = (x + 2)^2 - 4.
- The vertex form is y = a(x - h)^2 + k, where (h, k) represents the vertex. Here, the vertex is (-2, -4).
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