To find the missing step in the process, let's follow the given equations step-by-step and identify which option correctly fits into the sequence.
We start with the given equations:
[tex]\[ P = 17 - \sqrt{0.025x + 7} \][/tex]
It is then given:
[tex]\[ 25 = 17 - \sqrt{0.025x + 7} \][/tex]
Subtract 17 from both sides:
[tex]\[ 25 - 17 = -\sqrt{0.025x + 7} \][/tex]
[tex]\[ 8 = -\sqrt{0.025x + 7} \][/tex]
Next, we want to isolate the square root term:
[tex]\[ 8 = -\sqrt{0.025x + 7} \][/tex]
Multiply both sides by -1:
[tex]\[ -8 = \sqrt{0.025x + 7} \][/tex]
We see that this step directly matches option B. For completeness, let's validate the rest of the steps to ensure this is the correct missing step.
Continuing from:
[tex]\[ -8 = \sqrt{0.025x + 7} \][/tex]
Square both sides to eliminate the square root:
[tex]\[ (-8)^2 = (\sqrt{0.025x + 7})^2 \][/tex]
[tex]\[ 64 = 0.025x + 7 \][/tex]
Finally, isolate [tex]\(x\)[/tex] by subtracting 7 from both sides:
[tex]\[ 64 - 7 = 0.025x \][/tex]
[tex]\[ 57 = 0.025x \][/tex]
And solve for [tex]\(x\)[/tex] by dividing both sides by 0.025:
[tex]\[ x = \frac{57}{0.025} \][/tex]
[tex]\[ x = 2280 \][/tex]
Since option B correctly fits into the solution sequence without any discrepancy, we conclude that:
The missing equation is:
[tex]\[
\boxed{-8 = \sqrt{0.025 x + 7}}
\][/tex]
Thus, the correct answer is option B.
