Question

(165 +2х)^2 =(22х +153)^2=​

Answer 1

$(165 + 2x) {}^{2} = 165 {}^{2} + 2 \times 165 \times 2x + (2x) {}^{2} \\ 27225 + 660x + 4x {}^{2}$

делал по формуле (a+b)²=a²+2ab+b²

$(22x + 153) {}^{2} \\ (22x) {}^{2} + 2 \times 22x \times 153 + 153 {}^{2} \\ 484x {}^{2} + 6732x + 23409$

делал 2-ое по такой же формуле

Answer 2

$\displaystyle 1)(165+2x)^2=165^2+2x*165*2x+(2x)^2=27225+660x+4x^2\\\\ 2)(22x+153)^2=(22x)^2+2*22x*153+153^2=484x^2+6732x+23409$

Answer 3

To solve the equation $(165 + 2x)^2 = (22x + 153)^2$, you can first expand both sides of the equation and then simplify it. Here's the step-by-step solution:

1. Expand both sides of the equation: $(165 + 2x)^2 = (22x + 153)^2$

Expanding the left side: $(165 + 2x)^2 = 165^2 + 2(165)(2x) + (2x)^2$ $= 27225 + 660x + 4x^2$

Expanding the right side: $(22x + 153)^2 = (22x)^2 + 2(22x)(153) + 153^2$ $= 484x^2 + 6696x + 23409$

Now, your equation becomes: $27225 + 660x + 4x^2 = 484x^2 + 6696x + 23409$

2. Rearrange the equation so that all terms are on one side: $4x^2 + 660x + 27225 - 484x^2 - 6696x - 23409 = 0$

3. Combine like terms: $4x^2 - 484x^2 + 660x - 6696x + 27225 - 23409 = 0$

Simplify further: $-480x^2 - 6036x + 3824 = 0$

4. Divide the entire equation by -4 to simplify it further: $120x^2 + 1509x - 956 = 0$

5. Now, you can solve this quadratic equation. You can either use the quadratic formula or factor it if possible. In this case, let's use the quadratic formula:

The quadratic formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this equation, $a = 120$, $b = 1509$, and $c = -956$.

Now, plug these values into the quadratic formula:

$x = \frac{-1509 \pm \sqrt{1509^2 - 4(120)(-956)}}{2(120)}$

Calculate the discriminant ($b^2 - 4ac$) first:

$1509^2 - 4(120)(-956) = 2289481$

Now, plug it back into the formula:

$x = \frac{-1509 \pm \sqrt{2289481}}{240}$

Calculate the square root:

$x = \frac{-1509 \pm 1511}{240}$

Now, you have two possible solutions:

1. $x = \frac{-1509 + 1511}{240} = \frac{2}{240} = \frac{1}{120}$
2. $x = \frac{-1509 - 1511}{240} = \frac{-3020}{240} = -\frac{151}{12}$

So, the solutions for the equation $(165 + 2x)^2 = (22x + 153)^2$ are $x = \frac{1}{120}$ and $x = -\frac{151}{12}$.