Question

Решите уравнение: (x+4)^2=25

Answer 1

$(x+4)^{2}=25\\1)x+4=5\\x=1\\2)x+4=-5\\x=-9$

Ответ: -9; 1

Answer 2

(x + 4)² = 25,

x² + 16 + 8x = 25,

x² + 8x - 9 = 0.

D = b² - 4ac = 8² - 4 * 1 * (-9) = 64 + 36 = 100 = 10².

$x_{1} = \frac{-b + \sqrt{D}}{2a} = \frac{-8 + 10}{2*1} = \frac{2}{2} = 1,$

$x_{2} = \frac{-b - \sqrt{D}}{2a} = \frac{-8 - 10}{2*1} = \frac{-18}{2} = -9.$

Ответ: 1, -9.

Answer 3

To solve the equation (x + 4)^2 = 25, follow these steps:

Step 1: Expand the left side of the equation: (x + 4)^2 = (x + 4)(x + 4) = x^2 + 8x + 16

Step 2: Set the expanded equation equal to 25: x^2 + 8x + 16 = 25

Step 3: Move all terms to one side of the equation to set it to zero: x^2 + 8x + 16 - 25 = 0

Step 4: Simplify the equation: x^2 + 8x - 9 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = 8, and c = -9.

Step 5: Solve the quadratic equation using factoring or the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values: x = (-(8) ± √(8^2 - 4 * 1 * (-9))) / 2 * 1 x = (-8 ± √(64 + 36)) / 2 x = (-8 ± √100) / 2 x = (-8 ± 10) / 2

Now, we get two possible values for x:

1. When x = (-8 + 10) / 2: x = 2 / 2 x = 1

2. When x = (-8 - 10) / 2: x = -18 / 2 x = -9

So, the solutions to the equation are x = 1 and x = -9.