[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
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1.
[tex]kx^{2} + kx + \frac{25}{4}[/tex]
All you need to do is factor out [tex] \frac{1}{4}[/tex]
=[tex] \frac{4kx^{2 +} + 4kx + 25 } {4} [/tex]
if you evaluate it it will become
[tex]kx^{2} + kx + \frac{25}{4} [/tex]
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2.
[tex] \frac{3y² + 1}{4} - \frac{y}{2} = 6[/tex]
[tex]3y² + 1 - 2y = 24[/tex]
[tex]3y² - 23 - 2y = 0[/tex]
[tex]3y² - 2y - 23 = 0[/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 3\left(-23\right)}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{4-4\times 3\left(-23\right)}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{4-12\left(-23\right)}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{4+276}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{280}}{2\times 3}[/tex]
[tex]y=\frac{-\left(-2\right)±2\sqrt{70}}{2\times 3}[/tex]
[tex]y=\frac{2±2\sqrt{70}}{6}[/tex]
[tex]y=\frac{2\sqrt{70}+2}{6}[/tex]
[tex]y=\frac{\sqrt{70}+1}{3}[/tex]
[tex]y=\frac{2-2\sqrt{70}}{6}[/tex]
[tex]y=\frac{1-\sqrt{70}}{3}[/tex]
[tex]y=\frac{\sqrt{70}+1}{3}[/tex]
So the answer is
[tex]y=\frac{\sqrt{70}+1}{3}[/tex]
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Explanation:
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