Question

(3x-2)^2-(x-15)^2=0​

Answer 1

Ответ:

откроем скобки

$9 {x}^{2} - 12x + 4 - {x}^{2} + 30 x - 225 = 0$

Приведем подобные члены

$8 {x}^{2} + 18x - 221 = 0$

$d = {18}^{2} - 4 \times 8 \times ( - 221)=7396$

$x (1) = -\frac{ - 18 - \sqrt{7396} }{2 \times 8} = - \frac{13}{2}$

$x (2) = -\frac{ - 18 + \sqrt{7396} }{2 \times 8} = \frac{17}{4}$

Answer 2

The given equation is a quadratic equation involving two squared terms that are being subtracted from each other. Let's solve it step by step:

Given equation: (3x - 2)^2 - (x - 15)^2 = 0

First, let's expand both squared terms: (3x - 2)^2 = (3x - 2)(3x - 2) = 9x^2 - 12x + 4 (x - 15)^2 = (x - 15)(x - 15) = x^2 - 30x + 225

Substitute these expanded expressions back into the original equation: (9x^2 - 12x + 4) - (x^2 - 30x + 225) = 0

Now, combine like terms: 9x^2 - 12x + 4 - x^2 + 30x - 225 = 0 8x^2 + 18x - 221 = 0

Now you have a quadratic equation in standard form: 8x^2 + 18x - 221 = 0

You can solve this quadratic equation using various methods, such as factoring, completing the square, or using the quadratic formula. If you're looking for the solutions, you can either factor the quadratic expression or use the quadratic formula:

Quadratic Formula: For a quadratic equation ax^2 + bx + c = 0, the solutions are given by: x = (-b ± √(b^2 - 4ac)) / (2a)

In your equation, a = 8, b = 18, and c = -221. Plugging these values into the quadratic formula: x = (-18 ± √(18^2 - 4 * 8 * -221)) / (2 * 8) x = (-18 ± √(324 + 7088)) / 16 x = (-18 ± √7412) / 16

At this point, √7412 ≈ 86.104. So, you have two possible solutions: x = (-18 + 86.104) / 16 ≈ 4.257 x = (-18 - 86.104) / 16 ≈ -7.632

Therefore, the solutions to the equation are approximately 4.257 and -7.632.