Question

(x-2)₂-5(x-3)(x+3)+4(x-1)(x+4)=1

Answer 1

X^2-4x+4-5(x^2-9)+(4x-4)*(x+4)=1
x^2-4x+4-5x^2+45+4x^2+16x-4x-16=1
8x+33=1
8x=1-33
8x=-32
x=-4

Answer 2

Let's simplify and solve the given equation step by step:

(x - 2)₂ - 5(x - 3)(x + 3) + 4(x - 1)(x + 4) = 1

First, let's expand the expressions within the parentheses:

(x - 2)₂ - 5(x² - 9) + 4(x² + 3x - 4)

Now distribute the coefficients:

(x - 2)₂ - 5x² + 45 + 4x² + 12x - 16

Combine like terms:

x² - 2 - 5x² + 4x² + 12x + 45 - 16

Simplify further:

-4x² + 12x + 27

Now, let's rearrange the equation:

-4x² + 12x + 27 = 1

Subtract 1 from both sides:

-4x² + 12x + 27 - 1 = 0

Simplify:

-4x² + 12x + 26 = 0

Divide the entire equation by -2 to simplify the coefficients:

2x² - 6x - 13 = 0

Now, we can solve this quadratic equation. However, it appears to have complex roots, so we'll use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 2, b = -6, and c = -13. Plugging in these values, we get:

x = (-(-6) ± √((-6)² - 4 * 2 * -13)) / (2 * 2)

Simplifying further:

x = (6 ± √(36 + 104)) / 4

x = (6 ± √140) / 4

x = (6 ± 2√35) / 4

Simplifying the expression:

x = (3 ± √35) / 2

So the solutions to the equation are:

x = (3 + √35) / 2 x = (3 - √35) / 2