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Use the Quadratic Formula to determine the solution(s) to
0=2x^(2)-3x-5.

$11$ ) Use the Quadratic Formula to determine the solution(s) to $0=2 x^{2}-3 x-5$ .

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Quadratic equation with complex roots

Full solution

Q.

11

) Use the Quadratic Formula to determine the solution(s) to

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

.

Identify coefficients: Identify coefficients $a$ , $b$ , and $c$ in the equation $2x^2 - 3x - 5 = 0$ . $a = 2$ , $b = -3$ , $c = -5$
Substitute into Quadratic Formula: Substitute $a$ , $b$ , and $c$ into the Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . $\newline$ $x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot2\cdot(-5)}}{2\cdot2}$
Simplify terms and constants: Simplify the terms inside the square root and the constants outside. $x = \frac{3 \pm \sqrt{9 + 40}}{4}$
Add numbers under square root: Add the numbers under the square root. $x = \frac{3 \pm \sqrt{49}}{4}$
Take square root of $49$ : Take the square root of $49$ . $x = \frac{3 \pm 7}{4}$
Split into two solutions: Split into two separate solutions for the $\pm$ . $\newline$ $x = (3 + 7) / 4$ and $x = (3 - 7) / 4$
Simplify both solutions: Simplify both solutions. $\newline$ $x = \frac{10}{4}$ and $x = \frac{-4}{4}$ $\newline$ $x = 2.5$ and $x = -1$

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