Required $\newline$ $0//8$ $\newline$ $\newline$ Use the Quadratic Formula to solve the quadratic below $100$ $\newline$ $x^{2}-5x+9=0$ $\newline$ Desmos Scientific Calculator $\newline$ Show Your Work

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Q. Required

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0//8

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Use the Quadratic Formula to solve the quadratic below

100

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x^{2}-5x+9=0

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Desmos Scientific Calculator

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Show Your Work

Write Quadratic Formula: Write down the quadratic formula. $\newline$ The quadratic formula is used to find the solutions to a quadratic equation $ax^2 + bx + c = 0$ . The formula is: $\newline$ $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Identify Coefficients: Identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation $x^2 - 5x + 9 = 0$ . $\newline$ In this equation, $a = 1$ , $b = -5$ , and $c = 9$ .
Substitute into Formula: Substitute the coefficients into the quadratic formula. $\newline$ $x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(9)}}{2(1)}$ $\newline$ $x = \frac{5 \pm \sqrt{25 - 36}}{2}$
Simplify Discriminant: Simplify the expression under the square root (the discriminant). $\newline$ $x = \frac{5 \pm \sqrt{-11}}{2}$ $\newline$ Since the discriminant is negative, there are no real solutions to the equation, only complex solutions.
Write Complex Solutions: Write down the complex solutions. $\newline$ $x = \frac{5 \pm \sqrt{-11}}{2}$ $\newline$ $x = \frac{5 \pm i\sqrt{11}}{2}$