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Solve.
3x-9x^(2)=-10
Choose 1 answer:
(A) x=(7+-sqrt77)/(2)
(B) x=(-2+-sqrt13)/(-3)
(C) x=(-5+-sqrt305)/(14)
(D) x=(-1+-sqrt41)/(-6)

Solve. $\newline$ $3 x-9 x^{2}=-10$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{7 \pm \sqrt{77}}{2}$ $\newline$ (B) $x=\frac{-2 \pm \sqrt{13}}{-3}$ $\newline$ (C) $x=\frac{-5 \pm \sqrt{305}}{14}$ $\newline$ (D) $x=\frac{-1 \pm \sqrt{41}}{-6}$

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Add and subtract polynomials

Full solution

Q. Solve.

\newline

3 x-9 x^{2}=-10

\newline

Choose

1

answer:

\newline

(A)

x=\frac{7 \pm \sqrt{77}}{2}

\newline

(B)

x=\frac{-2 \pm \sqrt{13}}{-3}

\newline

(C)

x=\frac{-5 \pm \sqrt{305}}{14}

\newline

(D)

x=\frac{-1 \pm \sqrt{41}}{-6}

Rewrite Equation: Rewrite the equation in standard quadratic form. $\newline$ To solve the quadratic equation, we need to set it to zero by moving all terms to one side. $\newline$ $3x - 9x^2 = -10$ $\newline$ Add $9x^2$ and subtract $3x$ from both sides to get: $\newline$ $9x^2 - 3x + 10 = 0$
Identify Coefficients: Identify the coefficients for the quadratic formula. $\newline$ The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$ . $\newline$ In our equation, $9x^2 - 3x + 10 = 0$ , $a = 9$ , $b = -3$ , and $c = 10$ .
Substitute into Formula: Substitute the coefficients into the quadratic formula. $\newline$ $x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 9 \cdot 10}}{2 \cdot 9}$ $\newline$ $x = \frac{3 \pm \sqrt{9 - 360}}{18}$ $\newline$ $x = \frac{3 \pm \sqrt{-351}}{18}$
Simplify Square Root: Simplify the expression under the square root. Since the expression under the square root is negative ( $-351$ ), we have no real solutions. The equation has complex solutions because the discriminant ( $b^2 - 4ac$ ) is less than zero.
Write Complex Solutions: Write the complex solutions. $\newline$ The complex solutions can be written as: $\newline$ $x = \frac{3 \pm \sqrt{-351}}{18}$ $\newline$ $x = \frac{3 \pm i\sqrt{351}}{18}$ $\newline$ Since none of the answer choices are in the form of a complex number, we have made a mistake. We need to recheck our calculations.

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