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)

Rearrange Equation: First, we need to rearrange the equation into standard quadratic form, which is ax^2 + bx + c = 0. To do this, we add 9x^2 to both sides and add 10 to both sides of the equation. 3x - 9x^2 = -10 9x^2 - 3x + 10 = 0Use Quadratic Formula: Now that we have the quadratic equation in standard form, we can use the quadratic formula to find the solutions for x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c = 0. In our case, a = 9, b = -3, and c = 10.Calculate Discriminant: Next, we calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. Discriminant = (-3)^2 - 4(9)(10) Discriminant = 9 - 360 Discriminant = -351Identify Complex Solutions: Since the discriminant is negative (-351), there are no real solutions to the equation. The solutions are complex numbers. However, none of the answer choices (A, B, C, D) provided are complex numbers, which means there might be a mistake in the problem statement or the answer choices.

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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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Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

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}

Rearrange Equation: First, we need to rearrange the equation into standard quadratic form, which is $ax^2 + bx + c = 0$ . To do this, we add $9x^2$ to both sides and add $10$ to both sides of the equation. $\newline$ $3x - 9x^2 = -10$ $\newline$ $9x^2 - 3x + 10 = 0$
Use Quadratic Formula: Now that we have the quadratic equation in standard form, we can use the quadratic formula to find the solutions for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients from the quadratic equation $ax^2 + bx + c = 0$ . In our case, $a = 9$ , $b = -3$ , and $c = 10$ .
Calculate Discriminant: Next, we calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . $\newline$ Discriminant = $(-3)^2 - 4(9)(10)$ $\newline$ Discriminant = $9 - 360$ $\newline$ Discriminant = $-351$
Identify Complex Solutions: Since the discriminant is negative ( $-351$ ), there are no real solutions to the equation. The solutions are complex numbers. However, none of the answer choices ( $A$ , $B$ , $C$ , $D$ ) provided are complex numbers, which means there might be a mistake in the problem statement or the answer choices.