Question

4(10x-10)^2-8(10x-10)+4=0

Answer 1

Відповідь:

Пояснення:

Answer 2

To solve the quadratic equation 4(10x-10)^2 - 8(10x-10) + 4 = 0, we can simplify and solve it step by step.

Let's start by expanding and simplifying the equation:

4(10x-10)^2 - 8(10x-10) + 4 = 0

First, let's simplify the terms within the parentheses:

4(100x^2 - 200x + 100) - 8(10x - 10) + 4 = 0

Now distribute and simplify:

400x^2 - 800x + 400 - 80x + 80 + 4 = 0

Combine like terms:

400x^2 - 880x + 484 = 0

Now that we have a quadratic equation in standard form, we can solve it using various methods. One common method is factoring, but in this case, the equation does not factor easily.

Alternatively, we can use the quadratic formula to find the solutions. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 400, b = -880, and c = 484. Substituting these values into the quadratic formula, we have:

x = (-(-880) ± √((-880)^2 - 4 * 400 * 484)) / (2 * 400)

Simplifying further:

x = (880 ± √(774400 - 774400)) / 800

x = (880 ± √0) / 800

Since the discriminant (√(b^2 - 4ac)) is zero, the quadratic equation has one real solution.

x = 880 / 800

Simplifying the fraction:

x = 11 / 10

Therefore, the solution to the equation 4(10x-10)^2 - 8(10x-10) + 4 = 0 is x = 11/10 or 1.1.