Distribute terms in parentheses: Distribute the 1.6 to both terms inside the parentheses. 1.6(y^2) + 1.6(5) = 13.4 y 1.6y^2 + 8 = 13.4 yRearrange to form quadratic equation: Rearrange the equation to set it to zero and form a quadratic equation. 1.6y^2 - 13.4 y + 8 = 0Use quadratic formula: Since the quadratic equation is not easily factorable, use the quadratic formula to solve for y. The quadratic formula is y = (-b ± √(b^2 - 4ac)) / (2a), where a = 1.6, b = -13.4, and c = 8.Calculate discriminant: Calculate the discriminant (b^2 - 4ac). Discriminant = (-13.4)^2 - 4(1.6)(8) Discriminant = 179.56 - 4(12.8) Discriminant = 179.56 - 51.2 Discriminant = 128.36Calculate possible values for y: Calculate the two possible values for y using the quadratic formula. y = (-(-13.4) ± √128.36) / (2 * 1.6) y = (13.4 ± √128.36) / 3.2Calculate positive root: Calculate the positive root. y = (13.4 + √128.36) / 3.2 y = (13.4 + 11.33) / 3.2 y = 24.73 / 3.2 y ≈ 7.73Calculate negative root: Calculate the negative root. y = (13.4 - √128.36) / 3.2 y = (13.4 - 11.33) / 3.2 y = 2.07 / 3.2 y ≈ 0.65

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$1.6\left(y^{2}+5\right)=13.4 y$

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1.6\left(y^{2}+5\right)=13.4 y

Distribute terms in parentheses: Distribute the $1.6$ to both terms inside the parentheses. $\newline$ $1.6(y^2) + 1.6(5) = 13.4 y$ $\newline$ $1.6y^2 + 8 = 13.4 y$
Rearrange to form quadratic equation: Rearrange the equation to set it to zero and form a quadratic equation. $\newline$ $1.6y^2 - 13.4 y + 8 = 0$
Use quadratic formula: Since the quadratic equation is not easily factorable, use the quadratic formula to solve for $y$ . The quadratic formula is $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 1.6$ , $b = -13.4$ , and $c = 8$ .
Calculate discriminant: Calculate the discriminant $b^2 - 4ac$ . $\newline$ Discriminant = $(-13.4)^2 - 4(1.6)(8)$ $\newline$ Discriminant = $179.56 - 4(12.8)$ $\newline$ Discriminant = $179.56 - 51.2$ $\newline$ Discriminant = $128.36$
Calculate possible values for y: Calculate the two possible values for y using the quadratic formula. $\newline$ $y = \frac{-(-13.4) \pm \sqrt{128.36}}{2 \times 1.6}$ $\newline$ $y = \frac{13.4 \pm \sqrt{128.36}}{3.2}$
Calculate positive root: Calculate the positive root. $\newline$ $y = \frac{13.4 + \sqrt{128.36}}{3.2}$ $\newline$ $y = \frac{13.4 + 11.33}{3.2}$ $\newline$ $y = \frac{24.73}{3.2}$ $\newline$ $y \approx 7.73$
Calculate negative root: Calculate the negative root. $\newline$ $y = \frac{13.4 - \sqrt{128.36}}{3.2}$ $\newline$ $y = \frac{13.4 - 11.33}{3.2}$ $\newline$ $y = \frac{2.07}{3.2}$ $\newline$ $y \approx 0.65$