Directions: Solve each irrational solutions. 9. x^(2)-2x-4=0

Write Given Quadratic Equation: Write down the given quadratic equation. The given equation is x^2 - 2x - 4 = 0. We need to solve for x.Use Quadratic Formula: Use the quadratic formula to solve for x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c = 0. For our equation, a = 1, b = -2, and c = -4.Substitute Coefficients: Substitute the coefficients into the quadratic formula. x = (-(-2) ± √((-2)^2 - 4(1)(-4))) / (2(1)) x = (2 ± √(4 + 16)) / 2 x = (2 ± √20) / 2Simplify Square Root: Simplify the square root and the equation. √20 can be simplified to 2√5 because 20 = 4 * 5 and √4 = 2. x = (2 ± 2√5) / 2 Now, divide both terms in the numerator by 2. x = 1 ± √5Write Final Solutions: Write down the final solutions. The solutions to the equation x^2 - 2x - 4 = 0 are x = 1 + √5 and x = 1 - √5, which are both irrational numbers.

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Directions: Solve each irrational solutions. $\newline$ $x^{2} - 2x - 4 = 0$

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Q. Directions: Solve each irrational solutions.

\newline

x^{2} - 2x - 4 = 0

Write Given Quadratic Equation: Write down the given quadratic equation. $\newline$ The given equation is $x^2 - 2x - 4 = 0$ . $\newline$ We need to solve for $x$ .
Use Quadratic Formula: Use the quadratic formula to solve for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients from the quadratic equation $ax^2 + bx + c = 0$ . For our equation, $a = 1$ , $b = -2$ , and $c = -4$ .
Substitute Coefficients: Substitute the coefficients into the quadratic formula. $\newline$ $x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-4)}}{2(1)}$ $\newline$ $x = \frac{2 \pm \sqrt{4 + 16}}{2}$ $\newline$ $x = \frac{2 \pm \sqrt{20}}{2}$
Simplify Square Root: Simplify the square root and the equation. $\newline$ $\sqrt{20}$ can be simplified to $2\sqrt{5}$ because $20 = 4 \times 5$ and $\sqrt{4} = 2$ . $\newline$ $x = \frac{2 \pm 2\sqrt{5}}{2}$ $\newline$ Now, divide both terms in the numerator by $2$ . $\newline$ $x = 1 \pm \sqrt{5}$
Write Final Solutions: Write down the final solutions. $\newline$ The solutions to the equation $x^2 - 2x - 4 = 0$ are $x = 1 + \sqrt{5}$ and $x = 1 - \sqrt{5}$ , which are both irrational numbers.