Answer:
x = -8 + sqrt(10) and x = -8 - sqrt(10)
Explanation:
The quadratic equation to be solved is:
2(x + 8)² + 9 = 29
First, we need to simplify the left-hand side of the equation by expanding the squared term:
2(x + 8)(x + 8) + 9 = 29
Simplifying further, we get:
2(x² + 16x + 64) + 9 = 29
Distributing the 2, we get:
2x² + 32x + 128 + 9 = 29
Combining like terms, we get:
2x² + 32x + 137 = 29
Subtracting 29 from both sides, we get:
2x² + 32x + 108 = 0
Dividing both sides by 2, we get:
x² + 16x + 54 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula :
The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).