Question

(x+4)²=(3x-2)(x-8) допоможіть будь ласка розв'язати рівняння

Answer 1

X²+8x+16-3x²+24x+2x-16=0
-2x²+34x=0
-2x(x-17)=0
x=0
x=17

Answer 2

I can help you solve this equation. Here are the steps:

1. Expand the left side of the equation using the formula (a+b)²=a²+2ab+b². You will get x²+8x+16=(3x-2)(x-8). 2. Expand the right side of the equation using the distributive property. You will get x²+8x+16=3x²-26x+16. 3. Subtract x²+8x+16 from both sides of the equation to get 0=2x²-34x. This is a quadratic equation in the form of ax²+bx+c=0, where a=2, b=-34, and c=0. 4. To solve a quadratic equation, you can use the quadratic formula: x=(-b±√(b²-4ac))/(2a). Plug in the values of a, b, and c to get x=(-(-34)±√((-34)²-4(2)(0)))/(2(2)). 5. Simplify the expression to get x=(34±√(1156))/4. The square root of 1156 is 34, so you can write x=(34±34)/4. 6. There are two possible values for x: x=(34+34)/4=17 or x=(34-34)/4=0. These are the solutions of the equation.

You can check your answers by plugging them back into the original equation and see if they make it true. For example, if x=17, then (x+4)²=(3x-2)(x-8) becomes (17+4)²=(3(17)-2)(17-8), which is 441=441, a true statement.

You can also use online calculators to solve equations, such as [GeoGebra](https://www.geogebra.org/solver), [Quickmath](https://quickmath.com/solve/), [Mathdf](https://mathdf.com/equ/uk/), or [Calculadora Online](https://www.calculadoraonline.com.br/equacoes). These tools can show you the steps and the solutions of various types of equations.