Question

X(2x-9)^2 -2x(15+x)^2=0

Answer 1

х(2х-9)²-2х(15+х)²=0

х(4х²-36х+81)-2х(225+30х+х²)=0

4х³-36х²+81х-450х-60х²-2х³=0

2х³-96х²-369х=0

Answer 2

To solve the quadratic equation $X(2x-9)^2 - 2x(15+x)^2 = 0$, we can follow these steps:

Step 1: Expand the squared terms. Step 2: Factor out common terms. Step 3: Set each factor equal to zero and solve for $x$.

Let's go through each step in detail:

Step 1: Expand the squared terms Expand $(2x-9)^2$ and $(15+x)^2$:

$(2x-9)^2 = 4x^2 - 36x + 81$

$(15+x)^2 = x^2 + 30x + 225$

Step 2: Factor out common terms The equation becomes:

$X(4x^2 - 36x + 81) - 2x(x^2 + 30x + 225) = 0$

Step 3: Set each factor equal to zero and solve for $x$ Now we have two terms, and we can set each term equal to zero and solve for $x$:

Term 1: $X(4x^2 - 36x + 81) = 0$ This term can be factored further: $4x^2 - 36x + 81 = (2x - 9)^2 = 0$

Solve for $x$: $2x - 9 = 0$ $2x = 9$ $x = \frac{9}{2}$

Term 2: $-2x(x^2 + 30x + 225) = 0$ This term can be factored by factoring out $-2x$: $-2x(x^2 + 30x + 225) = -2x(x + 15)^2 = 0$

Solve for $x$: $x + 15 = 0$ $x = -15$

So, the solutions for the equation are $x = \frac{9}{2}$ and $x = -15$.