Question

(×+13)²=(×+12)²+(×-5)²
Give it to me please :(​​

Answer 1

To solve the problem, we will use the law of signs, to solve the problem

Law of signs:

• - × - = +
• - × + = -
• + × - = -
• + × + = +

With the law of signs, we solve, but first we must know the following.

¿What are the equations?

We know that the equations are those mathematical expressions that are called in members and separated, by their equal sign, which these carry their known data and unknown or unknown data, these are related through their mathematical operations.

Solving problem:

• x² + 26x + 169 = x² + 24x + 144 + x² - 10x + 25
• x² + 26x + 169 = 2x² + 14x + 169
• x² + 26x - 2x² - 14x = 0
• -x² + 12x = 0
• 12x - x² = 0
• x (12 - x) = 0
• x = 0.12

So, the result of this equation is x = 0.12

¡Hope this helped!

Answer 2

x = 0, x = 12

Explanation:

Given equation:

`(x+13)^2=(x+12)^2+(x-5)^2`

Expand:

`\implies (x+13)(x+13)=(x+12)(x+12)+(x-5)(x-5)`

`\implies x^2+26x+169=x^2+24x+144+x^2-10x+25`

Collect and combine like terms on the right side of the equation:

`\implies x^2+26x+169=x^2+x^2+24x-10x+144+25`

`\implies x^2+26x+169=2x^2+14x+169`

Subtract 169 from both sides:

`\implies x^2+26x=2x^2+14x`

Subtract x² from both sides:

`\implies 26x=x^2+14x`

Subtract 26x from both sides:

`\implies 0=x^2-12x`

`\implies x^2-12x=0`

Factor out the common term x:

`\implies x(x-12)=0`

Apply the zero-product property:

`\implies x=0`

`\implies x-12=0 \implies x=12`

Solution:

• x = 0, x = 12