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
- Rearranging the Equation
Start with the equation: $$ 18^2 + x^2 = 35^2 $$
First, calculate $18^2$ and $35^2$.
- Calculating the Squares
Compute the squares:
- $18^2 = 324$
- $35^2 = 1225$
Now substitute these values back into the equation: $$ 324 + x^2 = 1225 $$
- Isolating x²
Now, isolate $x^2$ by subtracting $324$ from both sides: $$ x^2 = 1225 - 324 $$
- Calculating the Right Side
Now, calculate the right side: $$ x^2 = 901 $$
- Taking the Square Root
Finally, take the square root of both sides to solve for $x$: $$ x = \sqrt{901} $$
- 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.
