Solve using the quadratic formula. $\newline$ $7x^2 + 9x + 1 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $x =$ _ or $x =$ _

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Solve a quadratic equation using the quadratic formula

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Q. Solve using the quadratic formula.

\newline

7x^2 + 9x + 1 = 0

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

\newline

x =

_____ or

x =

_____

Identify Coefficients: To solve the quadratic equation $7x^2 + 9x + 1 = 0$ using the quadratic formula, we first need to identify the coefficients $a$ , $b$ , and $c$ from the equation, where $a$ is the coefficient of $x^2$ , $b$ is the coefficient of $x$ , and $c$ is the constant term. $\newline$ In this equation, $a = 7$ , $a$ $0$ , and $a$ $1$ .
Quadratic Formula: The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . We will use this formula to find the values of $x$ .
Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . $\newline$ Discriminant = $9^2 - 4(7)(1) = 81 - 28 = 53$ .
Find Solutions: Since the discriminant is positive, we will have two real and distinct solutions for $x$ . Now we will use the quadratic formula to find the two solutions for $x$ .
First Solution: First solution using the positive square root: $\newline$ $x = \frac{-9 + \sqrt{53}}{2 \times 7}$ $\newline$ $x = \frac{-9 + \sqrt{53}}{14}$
Second Solution: Second solution using the negative square root: $\newline$ $x = \frac{-9 - \sqrt{53}}{2 \times 7}$ $\newline$ $x = \frac{-9 - \sqrt{53}}{14}$
Simplify Solutions: Now we can simplify the solutions if possible. However, since $\sqrt{53}$ cannot be simplified to a simpler radical and the fractions cannot be reduced further, we will leave the solutions in this form or convert them to decimal form rounded to the nearest hundredth. $\newline$ First solution as a decimal: $\newline$ $x \approx (-9 + 7.28) / 14$ $\newline$ $x \approx -1.72 / 14$ $\newline$ $x \approx $-0$.$12$
Simplify Solutions: Now we can simplify the solutions if possible. However, since $\sqrt{53}$ cannot be simplified to a simpler radical and the fractions cannot be reduced further, we will leave the solutions in this form or convert them to decimal form rounded to the nearest hundredth.$\newline$First solution as a decimal:$\newline$$x \approx (-9 + 7.28) / 14$$\newline$$x \approx -1.72 / 14$$\newline$$x \approx -0.12$Second solution as a decimal:$\newline$$x \approx (-9 - 7.28) / 14$$\newline$$x \approx -16.28 / 14$$\newline$$x \approx -1.16$