Identify the quadratic equation: Identify the quadratic equation to be solved. The given quadratic equation is x^(2) + 5x + 3 = 0. We need to find the values of x that satisfy this equation.Use the quadratic formula: Use the quadratic formula to find the solutions. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. For our equation, a = 1, b = 5, and c = 3.Calculate the discriminant: Calculate the discriminant (b^2 - 4ac). The discriminant is the part of the quadratic formula under the square root, which is b^2 - 4ac. For our equation, it is (5)^2 - 4(1)(3) = 25 - 12 = 13.Apply the discriminant: Apply the discriminant to the quadratic formula. Now that we have the discriminant, we can find the solutions using the quadratic formula: x = (-5 ± √13) / (2 * 1).Simplify the solutions: Simplify the solutions. The solutions are x = (-5 + √13) / 2 and x = (-5 - √13) / 2.Check the solutions: Check the solutions for any mathematical errors. By substituting the solutions back into the original equation, we can verify that they satisfy the equation. This step is to ensure there are no math errors.

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$x^{2}+5 x+3=0$

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Algebra 2

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x^{2}+5 x+3=0

Identify the quadratic equation: Identify the quadratic equation to be solved. $\newline$ The given quadratic equation is $x^{2} + 5x + 3 = 0$ . We need to find the values of $x$ that satisfy this equation.
Use the quadratic formula: Use the quadratic formula to find the solutions. $\newline$ The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$ . For our equation, $a = 1$ , $b = 5$ , and $c = 3$ .
Calculate the discriminant: Calculate the discriminant $(b^2 - 4ac)$ . $\newline$ The discriminant is the part of the quadratic formula under the square root, which is $b^2 - 4ac$ . For our equation, it is $(5)^2 - 4(1)(3) = 25 - 12 = 13$ .
Apply the discriminant: Apply the discriminant to the quadratic formula. $\newline$ Now that we have the discriminant, we can find the solutions using the quadratic formula: $x = \frac{-5 \pm \sqrt{13}}{2 \times 1}$ .
Simplify the solutions: Simplify the solutions. $\newline$ The solutions are $x = \frac{-5 + \sqrt{13}}{2}$ and $x = \frac{-5 - \sqrt{13}}{2}$ .
Check the solutions: Check the solutions for any mathematical errors. $\newline$ By substituting the solutions back into the original equation, we can verify that they satisfy the equation. This step is to ensure there are no math errors.