Question

X²-12x+36=0 7x²-25x+13=0 5x²=9x+2 решите пж с пояснением

Answer 1

X²-12x+36=0 это формула (x-6)²=0

7x²-25x+13=0 
D=625-364=261
x1=$\frac{25- \sqrt{261} }{14}$
x2=$\frac{25+ \sqrt{261} }{14}$

5x²=9x+2
D=81+40=221
x1=$\frac{9- \sqrt{221} }{10}$
x2=$\frac{9+ \sqrt{221} }{10}$

Answer 2

Solving the Equation x² - 12x + 36 = 0

To solve the equation x² - 12x + 36 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, the equation is x² - 12x + 36 = 0, so we can identify that a = 1, b = -12, and c = 36. Plugging these values into the quadratic formula, we get:

x = (-(-12) ± √((-12)² - 4(1)(36))) / (2(1))

Simplifying further:

x = (12 ± √(144 - 144)) / 2

x = (12 ± √0) / 2

Since the discriminant (b² - 4ac) is equal to zero, the equation has only one solution. Simplifying further:

x = 12 / 2

x = 6

Therefore, the equation x² - 12x + 36 = 0 has one solution, which is x = 6.

Solving the Equation 7x² - 25x + 13 = 0

To solve the equation 7x² - 25x + 13 = 0, we can again use the quadratic formula. Comparing this equation to the general form ax² + bx + c = 0, we can identify that a = 7, b = -25, and c = 13. Plugging these values into the quadratic formula, we get:

x = (-(-25) ± √((-25)² - 4(7)(13))) / (2(7))

Simplifying further:

x = (25 ± √(625 - 364)) / 14

x = (25 ± √261) / 14

Therefore, the solutions for the equation 7x² - 25x + 13 = 0 are:

x = (25 + √261) / 14

x = (25 - √261) / 14

Solving the Equation 5x² = 9x + 2

To solve the equation 5x² = 9x + 2, we need to rearrange it into standard quadratic form, which is ax² + bx + c = 0. In this case, we have:

5x² - 9x - 2 = 0

We can now use the quadratic formula to find the solutions. Comparing this equation to the general form, we can identify that a = 5, b = -9, and c = -2. Plugging these values into the quadratic formula, we get:

x = (-(-9) ± √((-9)² - 4(5)(-2))) / (2(5))

Simplifying further:

x = (9 ± √(81 + 40)) / 10

x = (9 ± √121) / 10

x = (9 ± 11) / 10

Therefore, the solutions for the equation 5x² = 9x + 2 are:

x = (9 + 11) / 10

x = 2

x = (9 - 11) / 10

x = -0.2

Please note that the solutions are approximate values rounded to one decimal place.

I hope this explanation helps! Let me know if you have any further questions.