Solve. -7x^(2)+7x+1=-8 Choose 1 answer: (A) x=(-7+-sqrt301)/(-14) (B) x=-1,(7)/(10) (C) x=(2+-sqrt5)/(-2) (D) x=(1+-sqrt57)/(-8)

Bringing the equation to standard form: First, we need to bring the equation to standard quadratic form ax^2 + bx + c = 0 by adding 8 to both sides of the equation. -7x^2 + 7x + 1 + 8 = -8 + 8 -7x^2 + 7x + 9 = 0Identifying the coefficients: Now, we identify the coefficients a, b, and c from the quadratic equation -7x^2 + 7x + 9 = 0. a = -7 b = 7 c = 9Substituting values into the quadratic formula: Next, we substitute the values of a, b, and c into the quadratic formula, which is x = (-b ± sqrt(b^2 - 4ac)) / (2a). x = (-(7) ± sqrt((7)^2 - 4(-7)(9))) / (2(-7))Simplifying the expression under the square root: We simplify the expression under the square root (the discriminant). sqrt((7)^2 - 4(-7)(9)) = sqrt(49 + 252) = sqrt(301)Substituting the discriminant back into the quadratic formula: Now we substitute the discriminant back into the quadratic formula. x = (-7 ± sqrt(301)) / (-14)Matching the solution with the answer choices: We can see that the solution matches one of the given answer choices, which is (A) x = (-7 ± sqrt(301)) / (-14).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve.

-7x^(2)+7x+1=-8
Choose 1 answer:
(A)
x=(-7+-sqrt301)/(-14)
(B)
x=-1,(7)/(10)
(C)
x=(2+-sqrt5)/(-2)
(D)
x=(1+-sqrt57)/(-8)

Solve. $\newline$ $-7 x^{2}+7 x+1=-8$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{-7 \pm \sqrt{301}}{-14}$ $\newline$ (B) $x=-1, \frac{7}{10}$ $\newline$ (C) $x=\frac{2 \pm \sqrt{5}}{-2}$ $\newline$ (D) $x=\frac{1 \pm \sqrt{57}}{-8}$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

-7 x^{2}+7 x+1=-8

\newline

Choose

1

answer:

\newline

(A)

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

\newline

(B)

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

\newline

(C)

x=\frac{2 \pm \sqrt{5}}{-2}

\newline

(D)

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

Bringing the equation to standard form: First, we need to bring the equation to standard quadratic form $ax^2 + bx + c = 0$ by adding $8$ to both sides of the equation. $\newline$ $-7x^2 + 7x + 1 + 8 = -8 + 8$ $\newline$ $-7x^2 + 7x + 9 = 0$
Identifying the coefficients: Now, we identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation $-7x^2 + 7x + 9 = 0$ . $\newline$ $a = -7$ $\newline$ $b = 7$ $\newline$ $c = 9$
Substituting values into the quadratic formula: Next, we substitute the values of $a$ , $b$ , and $c$ into the quadratic formula, which is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . $\newline$ $x = \frac{{-(7) \pm \sqrt{{(7)^2 - 4(-7)(9)}}}}{{2(-7)}}$
Simplifying the expression under the square root: We simplify the expression under the square root (the discriminant). $\sqrt{(7)^2 - 4(-7)(9)} = \sqrt{49 + 252} = \sqrt{301}$
Substituting the discriminant back into the quadratic formula: Now we substitute the discriminant back into the quadratic formula. $\newline$ x = $\frac{{-7 \pm \sqrt{{301}}}}{{-14}}$
Matching the solution with the answer choices: We can see that the solution matches one of the given answer choices, which is (A) $x = \frac{-7 \pm \sqrt{301}}{-14}$ .