18^2 + x^2 = 35^2

Understand the Problem

The question is asking to solve the equation 18^(2) + x^(2) = 35^(2) for the variable x. This involves applying basic algebraic operations to isolate x.

Answer

$x \approx 30.0$
Answer for screen readers

The final answer is $x \approx 30.0$.

Steps to Solve

  1. Rearranging the Equation

Start with the equation: $$ 18^2 + x^2 = 35^2 $$

First, calculate $18^2$ and $35^2$.

  1. Calculating the Squares

Compute the squares:

  • $18^2 = 324$
  • $35^2 = 1225$

Now substitute these values back into the equation: $$ 324 + x^2 = 1225 $$

  1. Isolating x²

Now, isolate $x^2$ by subtracting $324$ from both sides: $$ x^2 = 1225 - 324 $$

  1. Calculating the Right Side

Now, calculate the right side: $$ x^2 = 901 $$

  1. Taking the Square Root

Finally, take the square root of both sides to solve for $x$: $$ x = \sqrt{901} $$

  1. Finding the Value of x

Now, find the value of $x$: $$ x \approx 30.0 $$

The final answer is $x \approx 30.0$.

More Information

The value of $x$ represents the length of a side in a right triangle when you use the Pythagorean theorem. In this case, 18 and 35 can be thought of as the lengths of the other two sides.

Tips

  • Forgetting to apply the square root to both sides of the equation.
  • Miscalculating the squares of the numbers or the final subtraction.
Thank you for voting!
Use Quizgecko on...
Browser
Browser