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Answer:
Step using Quadratic Formula
[tex]2y ^ { 2 } +8y=9 \\ 2y^{2}+8y=9 \\ 2y^{2}+8y-9=9-9 \\ 2y^{2}+8y-9=0 \\ \\ y=\frac{-8±\sqrt{8^{2}-4\times 2\left(-9\right)}}{2\times 2} \\ \\ y=\frac{-8±\sqrt{64-4\times 2\left(-9\right)}}{2\times 2} \\ \\ y=\frac{-8±\sqrt{64-8\left(-9\right)}}{2\times 2} \\ \\ y=\frac{-8±\sqrt{64+72}}{2\times 2} \\ \\ y=\frac{-8±\sqrt{136}}{2\times 2} \\ \\ y=\frac{-8±2\sqrt{34}}{2\times 2} \\ \\ y=\frac{-8±2\sqrt{34}}{4} \\ \\ y=\frac{2\sqrt{34}-8}{4} \\ \\ y=\frac{\sqrt{34}}{2}-2 \\ \\ y=\frac{-2\sqrt{34}-8}{4} \\ \\ y=-\frac{\sqrt{34}}{2}-2 \\ \\ y=\frac{\sqrt{34}}{2}-2 \\ y=-\frac{\sqrt{34}}{2}-2 [/tex]
Step for Completing the Square
[tex]2y ^ { 2 } +8y=9 \\ 2y ^ { 2 } +8y=9 \\ \\ \frac{2y^{2}+8y}{2}=\frac{9}{2} \\ \\ y^{2}+\frac{8}{2}y=\frac{9}{2} \\ \\ y^{2}+\frac{8}{2}y=\frac{9}{2} \\ \\ y^{2}+4y+2^{2}=\frac{9}{2}+2^{2} \\ y^{2}+4y+4=\frac{9}{2}+4 \\ y^{2}+4y+4=\frac{17}{2} \\ \left(y+2\right)^{2}=\frac{17}{2} \\ \\ \sqrt{\left(y+2\right)^{2}}=\sqrt{\frac{17}{2}} \\ \\ y+2=\frac{\sqrt{34}}{2} \\ y+2=-\frac{\sqrt{34}}{2} \\ \\ y=\frac{\sqrt{34}}{2}-2 \\ y=-\frac{\sqrt{34}}{2}-2 [/tex]
Step-by-step explanation: