Factoring, completing the square, the quadratic formula — all fine skills, all slower than they need to be when a graph is one keystroke away.
The move: Move it to one side, tap the x-intercepts.
Why it works: Once everything is on one side, “solve” literally means “where does this graph hit zero?” — and those x-intercepts are marked, tappable points.
The pattern
- Put everything on one side as y =
- Graph it
- Tap the x-intercepts → those are the solutions
Worked example: What is the sum of the solutions of x² = 7x − 10?
- Subtract the right side: x² − 7x + 10 = 0. Graph the left as y.
y=x^2-7x+10 - Tap the curve — gray dots on the x-axis at x = 2 and x = 5. Those ARE the solutions.
- 2 + 5 = 7. No factoring, no quadratic formula, no “did I drop a sign?”
Worked example 2: How many real solutions does x³ − 4x = 0 have?
- Already equals zero — just graph the left side.
y=x^3-4x - Count the x-axis crossings: x = −2, 0, and 2. Three crossings → three solutions.
Remember it on test day
Zeros are x-crossings. That's the whole cue — say it when you see this question type and the steps follow.
When this isn't the move
If the question wants an exact radical answer like x = 1 + √3, the tapped decimal tells you which choice — but a no-calculator section still wants the algebra.
Drill it until it's reflex
This move is one of Desvantage's 18 training modules: a plain-English lesson, a type-it-yourself walkthrough inside a live Desmos calculator, and a 100-question drill bank that deals ten fresh questions per round. The first two modules — plus the 12-question diagnostic — are free.