Simple Quadratic Equations

A quadratic equation contains a squared pronumeral. This NSW Year 8 maths subtopic (NESA outcome MA4‑EQU‑C‑01) covers equations of the form \(ax^2 = c\): get \(x^2\) on its own, then take the square root of both sides, remembering that \(x^2 = 49\) gives \(x = 7\) or \(x = -7\).

You will solve equations such as \(3x^2 + 8 = 35\) and \(\frac{x^2}{3} = 12\), explain why \(3x^2 = -27\) has no solution, and give answers exactly as a surd, like \(\pm\sqrt{13}\), or as a rounded decimal. You will also use formulas, finding a radius from \(A = \pi r^2\) or the time a dropped stone takes to fall, and reject the negative root when a length or time cannot be negative. It is part of Year 8 Equations.