Question

(2x – 7)2 – 7(7 – 2x) = 0.

Answer 1

(2х-7)2-7(7-2х)=0

4х-14-49+14х=0

18х-63=0

18Х=63

х=3.5

Answer 2

To solve the given equation (2x – 7)^2 – 7(7 – 2x) = 0, you can follow these steps:

Step 1: Expand the equation Expand both the squared term and the multiplication term:

(2x – 7)^2 = (2x – 7)(2x – 7) = 4x^2 – 28x + 49 7(7 – 2x) = 49 – 14x

So the equation becomes: 4x^2 – 28x + 49 - 49 + 14x = 0

Step 2: Simplify the equation Combine like terms:

4x^2 - 28x + 14x = 0

Simplify further:

4x^2 - 14x = 0

Step 3: Factor out the common term Factor out 2x from the terms:

2x(2x - 7) = 0

Step 4: Solve for x Set each factor equal to zero and solve for x:

2x = 0 -> x = 0 2x - 7 = 0 -> 2x = 7 -> x = 7/2

So, the solutions for the equation are x = 0 and x = 7/2.