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Use the Quadratic Formula to solve the quadratic below.
x^(2)-5x+9=0

Use the Quadratic Formula to solve the quadratic below. $\newline$ $x^{2}-5 x+9=0$

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Factor sums and differences of cubes

Full solution

Q. Use the Quadratic Formula to solve the quadratic below.

\newline

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

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. $x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(9)}}{2(1)}$
Simplify Equation: Simplify the equation. $\newline$ $x = \frac{5 \pm \sqrt{25 - 36}}{2}$ $\newline$ $x = \frac{5 \pm \sqrt{-11}}{2}$
Complex Number Solutions: Since the discriminant (the value under the square root) is negative, the solutions will be complex numbers. $\newline$ $x = \frac{5 \pm \sqrt{-11}}{2}$ $\newline$ $x = \frac{5 \pm i\sqrt{11}}{2}$
Write Final Solutions: Write the final solutions. $\newline$ The solutions to the quadratic equation $x^2 - 5x + 9 = 0$ are: $\newline$ $x = \frac{5 + i\sqrt{11}}{2}$ and $x = \frac{5 - i\sqrt{11}}{2}$

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