Question

(3x−4)2−(x−10)2=0. x=[ ] x= [ ]

Answer 1

Ответ:

6x-8-2x+20=0

4x=-12

x=-3

Объяснение:

Answer 2

To solve the equation, we'll first expand the expressions and then simplify to find the value(s) of 'x'.

Given equation: (3x - 4)^2 - (x - 10)^2 = 0

Step 1: Expand the expressions (3x - 4)^2 = (3x - 4)(3x - 4) = 9x^2 - 24x + 16

(x - 10)^2 = (x - 10)(x - 10) = x^2 - 20x + 100

Step 2: Substitute the expanded expressions back into the equation and simplify: (9x^2 - 24x + 16) - (x^2 - 20x + 100) = 0

Step 3: Combine like terms on the left-hand side of the equation: 9x^2 - 24x + 16 - x^2 + 20x - 100 = 0

Step 4: Simplify the equation: 8x^2 - 4x - 84 = 0

Step 5: Now, we need to solve the quadratic equation for 'x'. We can use the quadratic formula to do this:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 8, b = -4, and c = -84.

Step 6: Substitute the values into the quadratic formula and solve for 'x': x = [(-(-4) ± √((-4)^2 - 4 * 8 * -84)) / 2 * 8]

x = [(4 ± √(16 + 2688)) / 16]

x = [(4 ± √2704) / 16]

Step 7: Calculate the two possible values of 'x': x = (4 + √2704) / 16 ≈ (4 + 52) / 16 ≈ 56 / 16 ≈ 3.5

x = (4 - √2704) / 16 ≈ (4 - 52) / 16 ≈ -48 / 16 ≈ -3

So, the two possible solutions for 'x' are x = 3.5 and x = -3.