Question

(x + 2)² + 2x = 5x (x - 2) плиз

Answer 1

Вот ответ с решением!

Answer 2

To solve the equation "(x + 2)² + 2x = 5x (x - 2)," we'll first expand and simplify both sides of the equation and then try to find the value(s) of x that satisfy the equation.

Step 1: Expand and simplify the equation. (x + 2)² + 2x = 5x (x - 2)

First, expand (x + 2)²: (x + 2)² = (x + 2)(x + 2) = x(x) + x(2) + 2(x) + 2(2) = x² + 2x + 2x + 4 = x² + 4x + 4

Now, substitute the expansion back into the equation: x² + 4x + 4 + 2x = 5x (x - 2)

Step 2: Bring all terms to one side of the equation: x² + 4x + 4 + 2x - 5x(x - 2) = 0

Step 3: Simplify the equation further: x² + 4x + 4 + 2x - 5x² + 10x = 0

Step 4: Combine like terms: -4x² + 16x + 4 = 0

Step 5: Now, we have a quadratic equation in standard form (ax² + bx + c = 0), where a = -4, b = 16, and c = 4. To find the values of x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values: x = (-(16) ± √((16)² - 4(-4)(4))) / 2(-4) x = (-16 ± √(256 + 64)) / (-8) x = (-16 ± √320) / (-8) x = (-16 ± √(16 * 20)) / (-8) x = (-16 ± 4√5) / (-8)

Now, split it into two separate solutions:

1. x = (-16 + 4√5) / (-8)
2. x = (-16 - 4√5) / (-8)

Step 6: Simplify the solutions further:

1. x = (16 - 4√5) / 8 (Divide both numerator and denominator by 4) x = (4 - √5) / 2

2. x = (16 + 4√5) / 8 (Divide both numerator and denominator by 4) x = (4 + √5) / 2

So, the solutions to the equation are: x = (4 - √5) / 2 x = (4 + √5) / 2