Question

(3х+5)(3х-5)-(3х-1)2=-4​

Answer 1

To solve this equation, we need to follow the order of operations (also known as PEMDAS) to simplify the expression on the left side of the equation.

First, let's simplify each part of the equation: (3x + 5)(3x - 5) can be expanded using the distributive property: = (9x^2 - 15x + 15x - 25) [Multiplying the terms within the parentheses] = (9x^2 - 25) [Combining like terms]

(3x - 1)2 can be simplified by multiplying: = 6x - 2 [Applying the distributive property]

Substituting these simplified expressions back into the original equation: (9x^2 - 25) - (6x - 2) = -4

Next, let's combine like terms: 9x^2 - 25 - 6x + 2 = -4 9x^2 - 6x - 23 = -4

Bringing all terms to one side, we get: 9x^2 - 6x - 23 + 4 = 0 9x^2 - 6x - 19 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. However, the given equation does not have rational roots, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 9, b = -6, and c = -19. Substituting these values into the quadratic formula: x = (-(-6) ± √((-6)^2 - 4(9)(-19))) / (2(9)) x = (6 ± √(36 + 684)) / 18 x = (6 ± √720) / 18 x = (6 ± 6√5) / 18 x = (1 ± √5) / 3

Therefore, the equation (3x+5)(3x-5)-(3x-1)2 = -4 has two solutions: x = (1 + √5) / 3 x = (1 - √5) / 3