Question

Решите уравнение(x-8)²=-32x​

Answer 1

Ответ:

x²-16x+64=32x

x²+16x+64=0

(x+8) ²=0

x+8=0

x=-8

Answer 2

Объяснение:

$(x - 8) {}^{2} = - 32x \\ x {}^{2} - 16x + 64 = - 32x \\ x {}^{2} - 16x + 64 + 32x = 0 \\ x {}^{2} + 16x + 64 = 0 \\ (x + 8) {}^{2} = 0 \\ x + 8 = 0 \\ x = - 8$

Answer 3

To solve the quadratic equation $(x - 8)^2 = -32x$, we first need to simplify the equation and then find the roots.

Step 1: Expand the squared term $(x - 8)^2$ using the formula $(a - b)^2 = a^2 - 2ab + b^2$:

$(x - 8)^2 = x^2 - 2(8)x + 8^2 = x^2 - 16x + 64$.

Step 2: Rewrite the equation with the expansion:

$x^2 - 16x + 64 = -32x$.

Step 3: Move all terms to one side of the equation to get it in standard quadratic form:

$x^2 - 16x + 32x + 64 = 0$.

Step 4: Combine like terms:

$x^2 - 16x + 32x + 64 = x^2 + 16x + 64 = 0$.

Step 5: Now we can solve this quadratic equation. There are multiple ways to solve it, but let's use the quadratic formula, which is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

For the equation $x^2 + 16x + 64 = 0$, the coefficients are: $a = 1$, $b = 16$, and $c = 64$.

Step 6: Substitute the coefficients into the quadratic formula:

$x = \frac{-16 \pm \sqrt{16^2 - 4(1)(64)}}{2(1)}$.

Step 7: Calculate the discriminant:

$D = b^2 - 4ac = 16^2 - 4(1)(64) = 256 - 256 = 0$.

Since the discriminant is zero, there is only one real root.

Step 8: Now, calculate the root:

$x = \frac{-16}{2} = -8$.

So, the solution to the equation $(x - 8)^2 = -32x$ is $x = -8$.