Question

X²+11x=(5-x)(5+x)-17​

Answer 1

x²+11x=(5-x)(5+x)-17​

x²+11х=25-x²-17

2x²+11х-8=0

a=2      D=121-4*2*-8=185

b=11      X1 = -11-√185/4 = -6,2

c=-8      Х2 = -11+√185/4 = 0,65

Ответ: -6,2; 0,65

Answer 2

To solve the quadratic equation $x^2 + 11x = (5 - x)(5 + x) - 17$, we can start by simplifying the right side of the equation:

$(5 - x)(5 + x) - 17 = 25 - x^2 - 17$

Now, we can rewrite the equation as:

$x^2 + 11x = 25 - x^2 - 17$

Next, let's move all the terms to one side of the equation to set it to zero:

$x^2 + 11x + x^2 - 25 + 17 = 0$

Combine like terms:

$2x^2 + 11x - 8 = 0$

Now, we have a quadratic equation in standard form ($ax^2 + bx + c = 0$). To solve for $x$, we can use the quadratic formula:

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

In this case, $a = 2$, $b = 11$, and $c = -8$. Plug these values into the quadratic formula:

$x = \frac{-11 \pm \sqrt{11^2 - 4(2)(-8)}}{2(2)}$

Now, calculate the discriminant ($b^2 - 4ac$):

$b^2 - 4ac = 11^2 - 4(2)(-8) = 121 + 64 = 185$

Now, substitute the discriminant back into the quadratic formula:

$x = \frac{-11 \pm \sqrt{185}}{4}$

So, there are two possible solutions for $x$:

1. $x = \frac{-11 + \sqrt{185}}{4}$
2. $x = \frac{-11 - \sqrt{185}}{4}$

These are the solutions to the quadratic equation $x^2 + 11x = (5 - x)(5 + x) - 17$.