Question

Решите уравнения, используя преобразование выделение полного квадрата двучлена: 2)х^2+12х+32=0 4)х^2-4х-45=0 Решите пожалуйста ! Заранее спасибо )

Answer 1

2)х^2+12х+32=0 
х² +2х*6 +36 -36 +32 = 0
(х+6)² = 4
х +6 = 2      или       х + 6 = -4
х = -4                        х = -10   
4)х^2-4х-45=0
х² -2*2 +4 -4 -45 = 0
(х-2)² = 49
х-2 = 7      или  х-2 = -7
х = 9                  х = -5 

Answer 2

Solving Equations using Completing the Square Method

To solve the given equations using the completing the square method, we will follow these steps:

1. Move the constant term to the other side of the equation. 2. Divide the coefficient of the x^2 term by 2 and square it. 3. Add the squared value obtained in step 2 to both sides of the equation. 4. Factor the perfect square trinomial on the left side of the equation. 5. Solve for x by taking the square root of both sides of the equation. 6. Simplify the square root expression and solve for x.

Let's solve the equations one by one.

Equation 2: x^2 + 12x + 32 = 0

Step 1: Move the constant term to the other side of the equation: x^2 + 12x = -32

Step 2: Divide the coefficient of the x^2 term by 2 and square it: (12/2)^2 = 36

Step 3: Add the squared value obtained in step 2 to both sides of the equation: x^2 + 12x + 36 = -32 + 36 (x + 6)^2 = 4

Step 4: Factor the perfect square trinomial on the left side of the equation: (x + 6)^2 = 2^2

Step 5: Solve for x by taking the square root of both sides of the equation: x + 6 = ±2

Step 6: Simplify the square root expression and solve for x: x = -6 ± 2 x = -8 or x = -4

Therefore, the solutions to the equation x^2 + 12x + 32 = 0 are x = -8 and x = -4.

Equation 4: x^2 - 4x - 45 = 0

Step 1: Move the constant term to the other side of the equation: x^2 - 4x = 45

Step 2: Divide the coefficient of the x^2 term by 2 and square it: (-4/2)^2 = 4

Step 3: Add the squared value obtained in step 2 to both sides of the equation: x^2 - 4x + 4 = 45 + 4 (x - 2)^2 = 49

Step 4: Factor the perfect square trinomial on the left side of the equation: (x - 2)^2 = 7^2

Step 5: Solve for x by taking the square root of both sides of the equation: x - 2 = ±7

Step 6: Simplify the square root expression and solve for x: x = 2 ± 7 x = 9 or x = -5

Therefore, the solutions to the equation x^2 - 4x - 45 = 0 are x = 9 and x = -5.

If you have any further questions, feel free to ask!