3(x − 4)² = 75 What are all the solutions to the given equation?

x = 4 − 5√3 and x = 4 + 5√3

Advanced Math

SAT nonlinear equations practice questions

Quadratics and other nonlinear equations. You factor, take square roots, count real solutions, and solve systems where a line meets a parabola.

Practice nonlinear equations 178 questions, no account needed.

Square roots come in pairs. Keeping only the positive root, or stopping at x + 6 = 7 without solving for x, are the usual mistakes.

Full skill name: Nonlinear equations in one variable and systems of equations

Pick an answer to check it and see why. Practice sets also have grid-ins, where you type the answer.

01Question 1
Easy
3(x − 4)² = 75 What are all the solutions to the given equation?
02Question 2
Medium
What are the solutions to (x + 6)² = 49?
03Question 3
Hard
√(x + 7) = x − 5 What is the solution set of the given equation?

Start a set in this skill. Every answer comes with an explanation.

178 questions in the bank: 33 Easy, 89 Medium, 56 Hard.