Solve. -6x=3x^(2)+1 Choose 1 answer: (A) x=(2+-4sqrt2)/(-7) (B) x=(5+-sqrt67)/(6) (C) x=(3+-sqrt6)/(-3) (D) x=-3+-2sqrt2

Rearranging the equation: First, we need to rearrange the equation into the standard quadratic form ax^2 + bx + c = 0. So we move all terms to one side of the equation to get: 3x^2 + 6x + 1 = 0Identifying the coefficients: Now, we identify the coefficients for the quadratic formula, where a = 3, b = 6, and c = 1.Applying the quadratic formula: Next, we apply the quadratic formula x = (-b ± sqrt(b^2 - 4ac)) / (2a). Substitute a = 3, b = 6, and c = 1 into the formula to get: x = (-(6) ± sqrt((6)^2 - 4(3)(1))) / (2(3))Simplifying the terms: Simplify the terms under the square root and the constants: x = (-6 ± sqrt(36 - 12)) / 6 x = (-6 ± sqrt(24)) / 6Factoring out perfect squares: We can simplify sqrt(24) by factoring out perfect squares: sqrt(24) = sqrt(4 * 6) = 2sqrt(6)Substituting back into the equation: Now, we substitute 2sqrt(6) back into the equation: x = (-6 ± 2sqrt(6)) / 6Dividing all terms by 2: We can simplify the equation by dividing all terms by 2: x = (-3 ± sqrt(6)) / 3Matching the solutions to answer choices: Finally, we can see that the solutions match one of the given answer choices: x = (-3 ± sqrt(6)) / 3 This corresponds to answer choice (C).

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Solve.

-6x=3x^(2)+1
Choose 1 answer:
(A)
x=(2+-4sqrt2)/(-7)
(B)
x=(5+-sqrt67)/(6)
(C)
x=(3+-sqrt6)/(-3)
(D)
x=-3+-2sqrt2

Solve. $\newline$ $-6 x=3 x^{2}+1$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{2 \pm 4 \sqrt{2}}{-7}$ $\newline$ (B) $x=\frac{5 \pm \sqrt{67}}{6}$ $\newline$ (C) $x=\frac{3 \pm \sqrt{6}}{-3}$ $\newline$ (D) $x=-3 \pm 2 \sqrt{2}$

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Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

-6 x=3 x^{2}+1

\newline

Choose

1

answer:

\newline

(A)

x=\frac{2 \pm 4 \sqrt{2}}{-7}

\newline

(B)

x=\frac{5 \pm \sqrt{67}}{6}

\newline

(C)

x=\frac{3 \pm \sqrt{6}}{-3}

\newline

(D)

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

Rearranging the equation: First, we need to rearrange the equation into the standard quadratic form $ax^2 + bx + c = 0$ . $\newline$ So we move all terms to one side of the equation to get: $\newline$ $3x^2 + 6x + 1 = 0$
Identifying the coefficients: Now, we identify the coefficients for the quadratic formula, where $a = 3$ , $b = 6$ , and $c = 1$ .
Applying the quadratic formula: Next, we apply the quadratic formula $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . $\newline$ Substitute $a = 3$ , $b = 6$ , and $c = 1$ into the formula to get: $\newline$ $x = \frac{{-(6) \pm \sqrt{{(6)^2 - 4(3)(1)}}}}{{2(3)}}$
Simplifying the terms: Simplify the terms under the square root and the constants: $\newline$ $x = \frac{{-6 \pm \sqrt{{36 - 12}}}}{6}$ $\newline$ $x = \frac{{-6 \pm \sqrt{{24}}}}{6}$
Factoring out perfect squares: We can simplify $\sqrt{24}$ by factoring out perfect squares: $\newline$ $\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}$
Substituting back into the equation: Now, we substitute $2\sqrt{6}$ back into the equation: $\newline$ $x = \frac{-6 \pm 2\sqrt{6}}{6}$
Dividing all terms by $2$ : We can simplify the equation by dividing all terms by $2$ : $\newline$ $x = \frac{{-3 \pm \sqrt{6}}}{{3}}$
Matching the solutions to answer choices: Finally, we can see that the solutions match one of the given answer choices: $\newline$ $x = \frac{{-3 \pm \sqrt{6}}}{{3}}$ $\newline$ This corresponds to answer choice (C).