Solving x: Quadratics -x^2+100=0 and 6x²-44=5x²-144 Compared

Let's solve each equation step-by-step:

1) Solve $-x^2 + 100 = 0$:

Step 1: Isolate $x^2$.

• Rearrange the equation to $x^2 = 100$.

Step 2: Solve for $x$ by taking the square root of both sides.

• $x = \pm \sqrt{100}$
• $x = \pm 10$

2) Solve $6x^2 - 44 = 5x^2 - 144$:

Step 1: Simplify by moving all terms to one side.

• $6x^2 - 5x^2 = -144 + 44$
• $x^2 = -100$

Step 2: Since $x^2 = -100$, there are no real solutions because we can't take the square root of a negative number in the set of real numbers.

Conclusion: From the solutions for our first equation, the possible values are $x = 10$ and $x = -10$. The largest $x$, since there are no real solutions from the second equation, is $x = 10$.