SAT Math Practice Question #2329 (Medium) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Medium

Digital SAT Math Practice Question #2329

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

If $\sqrt{x + 10} = x - 2$, what is the sum of all valid real solutions?
Select Your Answer:
Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
⚡ 15-Second Desmos Speed Hack

Desmos Hack: Graph the left and right sides of any equation to instantly view intersection points and filter out extraneous solutions.

Masterclass Solution & Distractor Trap Analysis

$x + 10 = x^2 - 4x + 4 \implies x^2 - 5x - 6 = 0 \implies (x - 6)(x + 1) = 0$. For $x = -1$, $\sqrt{9} \ne -3$ (extraneous). For $x = 6$, $\sqrt{16} = 4 = 6 - 2$ (valid). Only $x = 6$ is valid....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

🔒 Citadel Pro Scholar Vault

Unlock Full Solution & 2,600+ Official Drills

Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.

Socratic Assistant

Targeted hints without disclosing final solutions.

I am your Socratic tutor. Click one of the quick guidance buttons above or ask a specific question below about a formula or method.