Question

solve using the quadratic formula.
-9y² + 2 = 0
write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
y = or y =

Explanation:

Step1: Identify coefficients

For quadratic equation \(ay^2 + by + c = 0\), here \(a=-9\), \(b = 0\), \(c = 2\).

Step2: Apply quadratic formula

Quadratic formula: \(y=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(y=\frac{-0\pm\sqrt{0^2-4\times(-9)\times2}}{2\times(-9)}\)
Simplify inside square root: \(\sqrt{0 + 72}=\sqrt{72}=6\sqrt{2}\)
So \(y=\frac{\pm6\sqrt{2}}{-18}=\frac{\pm\sqrt{2}}{-3}=\mp\frac{\sqrt{2}}{3}\)
Calculate decimal: \(\sqrt{2}\approx1.414\), so \(y\approx-\frac{1.414}{3}\approx - 0.47\) or \(y\approx\frac{1.414}{3}\approx0.47\) (rounded to nearest hundredth)
Or fractional form: \(y = \frac{\sqrt{2}}{-3}=-\frac{\sqrt{2}}{3}\) and \(y=\frac{-\sqrt{2}}{-3}=\frac{\sqrt{2}}{3}\)

Answer:

\(y = \frac{\sqrt{2}}{3}\) or \(y = -\frac{\sqrt{2}}{3}\) (or approximately \(y = 0.47\) or \(y = - 0.47\))