Question

How do I solve for x?

Answer 1

Answer:

Using the Pythagorean Theorem - (leg #1)² + (leg #2)² = hypotenuse² - you can find that $x=17$.

Step-by-step explanation:

The Pythagorean Theorem states that, for every right triangle with legs a and b and hypotenuse c, these sides are related by the equation $a^2+b^2=c^2$. Using $x-2$ and 8 as our legs and $x$ as our hypotenuse, we can substitute to obtain the equation

$(x-2)^2+8^2=x^2$

From here, we can expand $(x-2)^2$ into the expression $x^2-4x+4$ and simplify 8² to 64, giving us

$x^2-4x+4+64=x^2$

Combining like terms:

$x^2-4x+68=x^2$

Since we have an $x^2$ on both sides, we can subtract it away to eliminate it:

$-4x+68=0$

Adding 4x to both sides:

$68=4x$

And finally dividing both sides by 4:

$17=x\\x=17$

Answer 2

Answer:

x=17

Step-by-step explanation:

The Pythagorean theorem

a^2 + b^2 =c^2  where a and b are the legs  and c is the hypotenuse

8^2 + (x-2)^2 = x^2

64 + (x-2)(x-2) = x^2

FOIL

64 + x^2 -2x-2x+4 = x^2

Combine like terms

68+x^2 -4x  = x^2

Subtract x^2 from each side

68+x^2-x^2 -4x  = x^2-x^2

68 -4x = 0

Add 4x to each side

68-4x+4x= 4x

68 = 4x

Divide by 4

68/4 = 4x/4

17 = x