Resolver las siguientes ecuaciobes, aplicando la formu general $$ \quad \frac{-b \pm \frac{\sqrt{b^{2}-4 a c}}{2 a}}{} \begin{array}{l} ext { a } \ ext { a) } 16 x^{2}-4 x-13=0\end{array} $$

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Resolver las siguientes ecuaciobes, aplicando la formu general $$ \quad \frac{-b \pm \frac{\sqrt{b^{2}-4 a c}}{2 a}}{} \begin{array}{l}	ext { a } \ 	ext { a) } 16 x^{2}-4 x-13=0\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ 16x^2-4x-13=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
  $$16x^{2}-4x-13=0$$
- step1: Solve using the quadratic formula:
  $$x=\frac{4\pm \sqrt{\left(-4ight)^{2}-4	imes 16\left(-13ight)}}{2	imes 16}$$
- step2: Simplify the expression:
  $$x=\frac{4\pm \sqrt{\left(-4ight)^{2}-4	imes 16\left(-13ight)}}{32}$$
- step3: Simplify the expression:
  $$x=\frac{4\pm \sqrt{848}}{32}$$
- step4: Simplify the expression:
  $$x=\frac{4\pm 4\sqrt{53}}{32}$$
- step5: Separate into possible cases:
  $$\begin{align}&x=\frac{4+4\sqrt{53}}{32}\&x=\frac{4-4\sqrt{53}}{32}\end{align}$$
- step6: Simplify the expression:
  $$\begin{align}&x=\frac{1+\sqrt{53}}{8}\&x=\frac{4-4\sqrt{53}}{32}\end{align}$$
- step7: Simplify the expression:
  $$\begin{align}&x=\frac{1+\sqrt{53}}{8}\&x=\frac{1-\sqrt{53}}{8}\end{align}$$
- step8: Rewrite:
  $$x_{1}=\frac{1-\sqrt{53}}{8},x_{2}=\frac{1+\sqrt{53}}{8}$$
Las soluciones de la ecuación $$16x^2-4x-13=0$$ son $$x_{1}=\frac{1-\sqrt{53}}{8}$$ y $$x_{2}=\frac{1+\sqrt{53}}{8}$$.
Las soluciones son $$x_{1}=\frac{1-\sqrt{53}}{8}$$ y $$x_{2}=\frac{1+\sqrt{53}}{8}$$.

Resolver las siguientes ecuaciobes, aplicando la formu general \( \quad \frac{-b \pm \frac{\sqrt{b^{2}-4 a c}}{2 a}}{} \begin{array}{l}\text { a } \\ \text { a) } 16 x^{2}-4 x-13=0\end{array} \)

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