For the given function and value of \( y \), find the corresponding value(s) of \( x \) : \( \begin{array}{ll}\text { a } y=x^{2}+6 x+10 & \text { when } y=1\end{array} \) b \( y=x^{2}+5 x+8 \)

Solve the equation \( x^{2}+6x+10=1 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(x^{2}+6x+10=1\) - step1: Move the expression to the left side: \(x^{2}+6x+9=0\) - step2: Factor the expression: \(\left(x+3\right)^{2}=0\) - step3: Simplify the expression: \(x+3=0\) - step4: Move the constant to the right side: \(x=0-3\) - step5: Remove 0: \(x=-3\) Solve the equation \( x^{2}+5x+8=1 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(x^{2}+5x+8=1\) - step1: Move the expression to the left side: \(x^{2}+5x+7=0\) - step2: Solve using the quadratic formula: \(x=\frac{-5\pm \sqrt{5^{2}-4\times 7}}{2}\) - step3: Simplify the expression: \(x=\frac{-5\pm \sqrt{-3}}{2}\) - step4: Simplify the expression: \(x=\frac{-5\pm \sqrt{3}\times i}{2}\) - step5: Separate into possible cases: \(\begin{align}&x=\frac{-5+\sqrt{3}\times i}{2}\\&x=\frac{-5-\sqrt{3}\times i}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=-\frac{5}{2}+\frac{\sqrt{3}}{2}i\\&x=\frac{-5-\sqrt{3}\times i}{2}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=-\frac{5}{2}+\frac{\sqrt{3}}{2}i\\&x=-\frac{5}{2}-\frac{\sqrt{3}}{2}i\end{align}\) - step8: Rewrite: \(x_{1}=-\frac{5}{2}-\frac{\sqrt{3}}{2}i,x_{2}=-\frac{5}{2}+\frac{\sqrt{3}}{2}i\) - step9: Remove the complex number(s): \(\textrm{No real solution}\) a) For the function \( y=x^{2}+6x+10 \) when \( y=1 \), the corresponding value of \( x \) is \( x=-3 \). b) For the function \( y=x^{2}+5x+8 \) when \( y=1 \), there is no real solution for \( x \).