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Solve for $x$ : $x^{2} + 3x - 10 = 0$ $a=1$ , $b=3$ , and $c=-10$ .

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Find derivatives using the product rule II

Full solution

Q. Solve for

x

:

x^{2} + 3x - 10 = 0

a=1

,

b=3

, and

c=-10

.

Identify type of equation: Identify the type of equation. $\newline$ The equation $x^2 + 3x - 10 = 0$ is a quadratic equation in the standard form $ax^2 + bx + c = 0$ , where $a = 1$ , $b = 3$ , and $c = -10$ .
Apply quadratic formula: Apply the quadratic formula to solve for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . We will use this formula to find the values of $x$ .
Calculate discriminant: Calculate the discriminant. $\newline$ The discriminant is the part of the quadratic formula under the square root, $b^2 - 4ac$ . Let's calculate it: $\newline$ Discriminant = $(3)^2 - 4(1)(-10) = 9 + 40 = 49$ .
Calculate possible values for x: Calculate the two possible values for x. $\newline$ Since the discriminant is positive, there will be two real solutions for x. $\newline$ $x = \frac{-3 \pm \sqrt{49}}{2 \times 1}$ $\newline$ $x = \frac{-3 \pm 7}{2}$
Solve for values of $x$ : Solve for the two values of $x$ . $\newline$ First solution: $\newline$ $x = (-3 + 7) / 2$ $\newline$ $x = 4 / 2$ $\newline$ $x = 2$ $\newline$ Second solution: $\newline$ $x = (-3 - 7) / 2$ $\newline$ $x = -10 / 2$ $\newline$ $x = -5$

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