Question

Решите уравнение. (x+7)^2 - (x-8)^2= -15

Answer 1

$(x+7)^2-(x-8)^2=-15\\x^2+14x+49-(x^2-16x+64)=-15\\x^2+14x+49-x^2+16x-64=-15\\14x+16x=-15+64-49\\30x=0\\x=0$

Answer 2

X^2+14x+49-x^2+16x-64=-15
30x-15=-15
30x=0
x=0

Answer 3

To solve the equation $(x+7)^2 - (x-8)^2 = -15$, let's first simplify the left side of the equation using the difference of squares formula:

$(a^2 - b^2) = (a + b)(a - b)$

Using this formula, we can rewrite the left side of the equation as:

$(x+7)^2 - (x-8)^2 = [(x+7) + (x-8)][(x+7) - (x-8)]$

Now, simplify the expression inside the brackets:

$(x+7) + (x-8) = 2x - 1$

$(x+7) - (x-8) = 2x + 15$

So, the equation becomes:

$(2x - 1)(2x + 15) = -15$

Now, distribute and expand:

$4x^2 + 28x - 2x - 15 = -15$

Combine like terms:

$4x^2 + 26x - 15 = -15$

Next, move all terms to one side to set the equation to zero:

$4x^2 + 26x - 15 + 15 = 0$

$4x^2 + 26x = 0$

Factor out the common term, which is 2x:

$2x(2x + 13) = 0$

Now, set each factor to zero and solve for x:

1. $2x = 0$

$x = 0$

2. $2x + 13 = 0$

$2x = -13$

$x = -\frac{13}{2}$

So, the solutions to the equation are $x = 0$ and $x = -\frac{13}{2}$.