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For the following quadratic equation, find the discriminant.

-3x^(2)-18 x-72=-2x^(2)
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-3 x^{2}-18 x-72=-2 x^{2}$ $\newline$ Answer:

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Solve exponential equations by rewriting the base

Full solution

Q. For the following quadratic equation, find the discriminant.

\newline

-3 x^{2}-18 x-72=-2 x^{2}

\newline

Answer:

Simplify Quadratic Equation: First, we need to simplify the quadratic equation by moving all terms to one side to get it into standard form $ax^2 + bx + c = 0$ .
$-3x^2 - 18x - 72 = -2x^2$
Add $2x^2$ to both sides to combine like terms.
$-3x^2 + 2x^2 - 18x - 72 = 0$
Combine Like Terms: Now, we simplify the equation further by combining the $x^2$ terms. $\newline$ $(-3x^2 + 2x^2) - 18x - 72 = 0$ $\newline$ $-1x^2 - 18x - 72 = 0$
Standard Form: We now have the quadratic equation in standard form, which is: $\newline$ $-1x^2 - 18x - 72 = 0$ $\newline$ To find the discriminant of a quadratic equation in the form $ax^2 + bx + c = 0$ , we use the formula $b^2 - 4ac$ .
Identify Coefficients: Identify the coefficients $a$ , $b$ , and $c$ from the equation $-1x^2 - 18x - 72 = 0$ . $a = -1$ , $b = -18$ , $c = -72$
Substitute Values: Substitute the values of $a$ , $b$ , and $c$ into the discriminant formula. $\text{Discriminant} = b^2 - 4ac$ $\text{Discriminant} = (-18)^2 - 4(-1)(-72)$
Calculate Discriminant: Calculate the discriminant. $\newline$ Discriminant = $324 - 4(1)(72)$ $\newline$ Discriminant = $324 - 288$
Final Result: Finish the calculation to find the value of the discriminant. $\newline$ Discriminant = $324 - 288$ $\newline$ Discriminant = $36$

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