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Solve using the quadratic formula. $\newline$ $2u^2 + 7u + 1 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $u =$ _ or $u =$ _

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Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve using the quadratic formula.

\newline

2u^2 + 7u + 1 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

u =

_____ or

u =

_____

Identify values: Identify the values of $a$ , $b$ , and $c$ in the quadratic equation $2u^2 + 7u + 1 = 0$ . The quadratic equation is in the form $au^2 + bu + c = 0$ . Here, $a = 2$ , $b = 7$ , and $c = 1$ .
Substitute values: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula $u = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Using $a = 2$ , $b = 7$ , and $c = 1$ , we get: $u = \frac{-(7) \pm \sqrt{(7)^2 - 4\cdot2\cdot1}}{2\cdot2}$
Simplify discriminant: Simplify the expression under the square root (the discriminant). $\sqrt{(7)^2 - 4\cdot 2\cdot 1} = \sqrt{49 - 8} = \sqrt{41}$
Substitute discriminant: Substitute the discriminant back into the quadratic formula. $\newline$ $u = \frac{-7 \pm \sqrt{41}}{4}$
Calculate possible values: Calculate the two possible values for $u$ . $\newline$ First solution: $\newline$ $u = \frac{{-7 + \sqrt{41}}}{{4}}$ $\newline$ Second solution: $\newline$ $u = \frac{{-7 - \sqrt{41}}}{{4}}$
Round values: Round the values of $u$ to the nearest hundredth, if necessary. $\newline$ First solution: $\newline$ $u \approx (-7 + 6.40) / 4$ $\newline$ $u \approx -0.60 / 4$ $\newline$ $u \approx -0.15$ $\newline$ Second solution: $\newline$ $u \approx (-7 - 6.40) / 4$ $\newline$ $u \approx -13.40 / 4$ $\newline$ $u \approx \(-3\).\(35\)

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