1) \( 2 x^{4}+9 x^{2}-68=0 \) 2) \( 18 x^{2}-2=0 \) \( 2-3 x \quad 3+2 x \)

Solve the equation \( 2x^4+9x^2-68=0 \). Solve the equation by following steps: - step0: Solve for \(x\): \(2x^{4}+9x^{2}-68=0\) - step1: Factor the expression: \(\left(x-2\right)\left(x+2\right)\left(2x^{2}+17\right)=0\) - step2: Separate into possible cases: \(\begin{align}&x-2=0\\&x+2=0\\&2x^{2}+17=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=2\\&x=-2\\&x \notin \mathbb{R}\end{align}\) - step4: Find the union: \(\begin{align}&x=2\\&x=-2\end{align}\) - step5: Rewrite: \(x_{1}=-2,x_{2}=2\) Solve the equation \( 18x^2-2=0 \). Solve the quadratic equation by following steps: - step0: Solve using square roots: \(18x^{2}-2=0\) - step1: Add or subtract both sides: \(18x^{2}=2\) - step2: Divide both sides: \(\frac{18x^{2}}{18}=\frac{2}{18}\) - step3: Divide the numbers: \(x^{2}=\frac{1}{9}\) - step4: Simplify the expression: \(x=\pm \sqrt{\frac{1}{9}}\) - step5: Simplify the expression: \(x=\pm \frac{1}{3}\) - step6: Separate into possible cases: \(\begin{align}&x=\frac{1}{3}\\&x=-\frac{1}{3}\end{align}\) - step7: Rewrite: \(x_{1}=-\frac{1}{3},x_{2}=\frac{1}{3}\) Las soluciones de las ecuaciones dadas son: 1) \( 2x^4+9x^2-68=0 \) tiene soluciones \( x=-2 \) y \( x=2 \). 2) \( 18x^2-2=0 \) tiene soluciones \( x=-\frac{1}{3} \) y \( x=\frac{1}{3} \).