Solve. 9=-7x+7x^(2) Choose 1 answer: (A) x=(-3+-2sqrt6)/(-3) (B) x=-1,(7)/(10) (c) x=(1+-sqrt57)/(-8) (D) x=(-7+-sqrt301)/(-14)

Identifying coefficients: Now that we have the equation in standard form, we can identify the coefficients a, b, and c. a = 7, b = -7, c = -9Using the quadratic formula: Next, we will use the quadratic formula to find the solutions for x. The quadratic formula is given by: x = (-b ± sqrt(b^2 - 4ac)) / (2a)Substituting values: We substitute the values of a, b, and c into the quadratic formula. x = (-(-7) ± sqrt((-7)^2 - 4*7*(-9))) / (2*7) x = (7 ± sqrt(49 + 252)) / 14 x = (7 ± sqrt(301)) / 14Simplifying the equation: Now we simplify the square root and the fraction. x = (7 ± sqrt(301)) / 14 Since sqrt(301) cannot be simplified further, we have two possible solutions for x: x = (7 + sqrt(301)) / 14 or x = (7 - sqrt(301)) / 14Checking the answer choices: We check the answer choices to see which one matches our solutions. (A) x = (-3 ± 2sqrt(6)) / (-3) does not match. (B) x = -1, 7/10 does not match. (C) x = (1 ± sqrt(57)) / (-8) does not match. (D) x = (-7 ± sqrt(301)) / (-14) matches our solutions after simplifying the negative signs.Correct answer: Therefore, the correct answer is (D) x = (-7 ± sqrt(301)) / (-14).

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9=-7x+7x^(2)
Choose 1 answer:
(A)
x=(-3+-2sqrt6)/(-3)
(B)
x=-1,(7)/(10)
(c)
x=(1+-sqrt57)/(-8)
(D)
x=(-7+-sqrt301)/(-14)

Solve. $\newline$ $9=-7 x+7 x^{2}$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{-3 \pm 2 \sqrt{6}}{-3}$ $\newline$ (B) $x=-1, \frac{7}{10}$ $\newline$ (C) $x=\frac{1 \pm \sqrt{57}}{-8}$ $\newline$ (D) $x=\frac{-7 \pm \sqrt{301}}{-14}$

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Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

9=-7 x+7 x^{2}

\newline

Choose

1

answer:

\newline

(A)

x=\frac{-3 \pm 2 \sqrt{6}}{-3}

\newline

(B)

x=-1, \frac{7}{10}

\newline

(C)

x=\frac{1 \pm \sqrt{57}}{-8}

\newline

(D)

x=\frac{-7 \pm \sqrt{301}}{-14}

Identifying coefficients: Now that we have the equation in standard form, we can identify the coefficients $a$ , $b$ , and $c$ . $a = 7$ , $b = -7$ , $c = -9$
Using the quadratic formula: Next, we will use the quadratic formula to find the solutions for x. The quadratic formula is given by: $\newline$ x = ( $-b \pm \sqrt{b^2 - 4ac}$ ) / ( $2a$ )
Substituting values: We substitute the values of $a$ , $b$ , and $c$ into the quadratic formula. $\newline$ $x = \frac{{-(-7) \pm \sqrt{{(-7)^2 - 4 \cdot 7 \cdot (-9)}}}}{{2 \cdot 7}}$ $\newline$ $x = \frac{{7 \pm \sqrt{{49 + 252}}}}{14}$ $\newline$ $x = \frac{{7 \pm \sqrt{{301}}}}{14}$
Simplifying the equation: Now we simplify the square root and the fraction. $\newline$ $x = \frac{7 \pm \sqrt{301}}{14}$ $\newline$ Since $\sqrt{301}$ cannot be simplified further, we have two possible solutions for x: $\newline$ $x = \frac{7 + \sqrt{301}}{14}$ or $x = \frac{7 - \sqrt{301}}{14}$
Checking the answer choices: We check the answer choices to see which one matches our solutions. $\newline$ (A) $x = \frac{-3 \pm 2\sqrt{6}}{-3}$ does not match. $\newline$ (B) $x = -1, \frac{7}{10}$ does not match. $\newline$ (C) $x = \frac{1 \pm \sqrt{57}}{-8}$ does not match. $\newline$ (D) $x = \frac{-7 \pm \sqrt{301}}{-14}$ matches our solutions after simplifying the negative signs.
Correct answer: Therefore, the correct answer is $D$ $x = \frac{{-7 \pm \sqrt{{301}}}}{{-14}}$ .