To solve the given expression, we will simplify it step-by-step.
The expression is:
[tex]\[5(x^2 - 1) - 5x^2 + x + 5 + \sqrt{100} + 2^2\][/tex]
First, let's simplify the square root and the exponentiation within the expression:
[tex]\[\sqrt{100} = 10\][/tex]
[tex]\[2^2 = 4\][/tex]
So the expression becomes:
[tex]\[5(x^2 - 1) - 5x^2 + x + 5 + 10 + 4\][/tex]
Now, let's distribute the 5 in the first term:
[tex]\[5(x^2 - 1) = 5x^2 - 5\][/tex]
Substituting this into the expression, we get:
[tex]\[5x^2 - 5 - 5x^2 + x + 5 + 10 + 4\][/tex]
Now, combine like terms. Combine all the constants together:
[tex]\[-5 + 5 + 10 + 4 = 14\][/tex]
So the expression simplifies to:
[tex]\[5x^2 - 5x^2 + x + 14\][/tex]
Notice that [tex]\(5x^2 - 5x^2\)[/tex] cancels out, leaving us with:
[tex]\[x + 14\][/tex]
Thus, the simplified form of the expression is:
[tex]\[x + 14\][/tex]
