Question

(х+5)(х-4)+х2+18=0 (х+7)(х-7)+(х-3)2=53

Answer 1

(х+5)(х-4)+х2+18=0

1) раскроем скобки
(х+5)(х-4)+х2+18=0

х2 - 4х + 5х - 20 - х2 + 18 = 0

2) решаем
x2-x2 = 0
-20+18=-2
x2+x-20-x2+18=0
x-20+18=0
x-2=0
х=2


(х+7)(х-7)+(х-3)2=53

(х^2-49)-(x^2-6x+9)=53

x^2-49-x^2+6x-9 = 53

6x= 53+9+49

6x=111
x= 111 : 6
х = 18.5

Answer 2

Let's solve the two equations:

1. (x + 5)(x - 4) + x^2 + 18 = 0

First, expand the expressions:

x^2 - 4x + 5x - 20 + x^2 + 18 = 0

Now, combine like terms:

2x^2 - 2x - 2 = 0

Divide the entire equation by 2 to simplify it:

x^2 - x - 1 = 0

Now, you can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = -1, and c = -1. Plug these values into the formula:

x = (-(-1) ± √((-1)² - 4(1)(-1))) / (2(1))

Simplify:

x = (1 ± √(1 + 4))/2

x = (1 ± √5)/2

So, the solutions for the first equation are:

x = (1 + √5)/2 x = (1 - √5)/2

Now, let's solve the second equation:

2. (x + 7)(x - 7) + (x - 3)^2 = 53

Expand the expressions:

x^2 - 49 + x^2 - 14x + 49 + x^2 - 6x + 9 = 53

Combine like terms:

3x^2 - 20x + 9 = 53

Subtract 53 from both sides:

3x^2 - 20x + 9 - 53 = 0

3x^2 - 20x - 44 = 0

Now, divide the equation by 1 (to simplify it further):

3x^2 - 20x - 44 = 0

Now, you can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 3, b = -20, and c = -44. Plug these values into the formula:

x = (20 ± √((-20)² - 4(3)(-44))) / (2(3))

Simplify:

x = (20 ± √(400 + 528)) / 6

x = (20 ± √928) / 6

Now, simplify further by finding the square root of 928:

x = (20 ± √(4 * 232)) / 6

x = (20 ± 4√58) / 6

Now, you can simplify by dividing both the numerator and denominator by 2:

x = (10 ± 2√58) / 3

So, the solutions for the second equation are:

x = (10 + 2√58)/3 x = (10 - 2√58)/3

These are the solutions for both equations.