Question

X²+6x+9= (x-5)(x+5)= (x+4)²= x²-36= x²-14x+49

Answer 1

Ответ:

${(x + 3)}^{2}$

${x^{2} - 25}$

${x}^{2} + 8x + 16$

${(x - 6)(x + 6)}$

${(x - 7)}^{2}$

Answer 2

1) (x+3)в квадрате
2) x в квадрате -25
3) x в квадрате +8x+16
4) (x-6)*(x+6)
5) (x-7) в квадрате

Answer 3

Let's analyze each equation separately:

1. x² + 6x + 9 = (x - 5)(x + 5): Expanding the right side using the distributive property, we have: (x - 5)(x + 5) = x(x) + x(5) - 5(x) - 5(5) = x² + 5x - 5x - 25 = x² - 25 So, the equation becomes: x² + 6x + 9 = x² - 25

By subtracting x² from both sides, we get: 6x + 9 = -25

Subtracting 9 from both sides: 6x = -34

Finally, dividing both sides by 6: x = -34/6 = -17/3

2. (x + 4)² = x² - 36: Expanding the left side using the square of a binomial, we have: (x + 4)² = (x + 4)(x + 4) = x(x) + x(4) + 4(x) + 4(4) = x² + 4x + 4x + 16 = x² + 8x + 16

So, the equation becomes: x² + 8x + 16 = x² - 36

By subtracting x² from both sides, we get: 8x + 16 = -36

Subtracting 16 from both sides: 8x = -52

Finally, dividing both sides by 8: x = -52/8 = -13/2 = -6.5

3. x² - 14x + 49: This equation does not match the others and is already in simplified form. It represents a perfect square trinomial, where (x - 7)² = x² - 14x + 49.

In summary:

1. x = -17/3
2. x = -6.5
3. (x - 7)² = x² - 14x + 49