This is a Pythagorean Theorem
x^2 + (2x + 4)^2 = (2x + 6)^2
no
so what are we doing with it?
Solving it ?
x^2 + 4x^2 + 16x + 16 = 4x^2+ 24x + 36
x^2 -8x -20 = 0
(x-10)(x+2) = 0
x = 10 or x = -2
but if x, 2x+4, and 2x+6 are the sides, then x = -2 makes no sense
so x = 10
check
sides would be 10, 24, and 26
which is twice the sides of the 5,12, 13 right-angled triangle, which I recognize to be right-angled.
So my answer is correct.
I was not asking if it was a Pythagorean Theorem? This is the equation that I have to solve
Thank you
To solve this equation, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In your equation, we have x^2 + (2x + 4)^2 = (2x + 6)^2. Let's solve it step by step:
1. Expand the squares:
x^2 + (2x + 4)(2x + 4) = (2x + 6)(2x + 6)
x^2 + (2x + 4)(2x + 4) = (4x^2 + 12x + 12x + 36)
x^2 + (2x + 4)(2x + 4) = (4x^2 + 24x + 36)
2. Simplify and combine like terms:
x^2 + 4x^2 + 8x + 8x + 16 = 4x^2 + 24x + 36
5x^2 + 16x + 16 = 4x^2 + 24x + 36
3. Move all terms to one side of the equation to set it to zero:
5x^2 + 16x + 16 - 4x^2 - 24x - 36 = 0
x^2 - 8x - 20 = 0
4. Factor the quadratic equation:
(x - 10)(x + 2) = 0
5. Solve for x by setting each factor equal to zero:
x - 10 = 0 or x + 2 = 0
6. Solve for x in each equation:
x = 10 or x = -2
Therefore, the solutions are x = 10 or x = -2.