Deber de mutematica - Resolver las siguientes ecuacioses a riicundo va cormula seneral sigvientes ecuaciobes \( \frac{x=-b \pm \sqrt{b^{2}-4 a c}}{2 a} \) a) \( \left.16 x^{2}-4 x-1\right]=0 \)

Solve the equation \( 16x^2 - 4x - 1 = 0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(16x^{2}-4x-1=0\) - step1: Solve using the quadratic formula: \(x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 16\left(-1\right)}}{2\times 16}\) - step2: Simplify the expression: \(x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 16\left(-1\right)}}{32}\) - step3: Simplify the expression: \(x=\frac{4\pm \sqrt{80}}{32}\) - step4: Simplify the expression: \(x=\frac{4\pm 4\sqrt{5}}{32}\) - step5: Separate into possible cases: \(\begin{align}&x=\frac{4+4\sqrt{5}}{32}\\&x=\frac{4-4\sqrt{5}}{32}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=\frac{1+\sqrt{5}}{8}\\&x=\frac{4-4\sqrt{5}}{32}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=\frac{1+\sqrt{5}}{8}\\&x=\frac{1-\sqrt{5}}{8}\end{align}\) - step8: Rewrite: \(x_{1}=\frac{1-\sqrt{5}}{8},x_{2}=\frac{1+\sqrt{5}}{8}\) Las soluciones de la ecuación \(16x^2 - 4x - 1 = 0\) son \(x_{1} = \frac{1-\sqrt{5}}{8}\) y \(x_{2} = \frac{1+\sqrt{5}}{8}\).