Solve. -4+x+7x^(2)=0 Choose 1 answer: (A) x=(-7+-sqrt65)/(8) (B) x=(-1+-sqrt5)/(2) (C) x=(-1+-sqrt113)/(14) (D) x=(3+-sqrt21)/(6)

Rewriting the equation: First, let's rewrite the equation in standard quadratic form, which is $ ax^2 + bx + c = 0 $. The given equation is $ -4 + x + 7x^2 = 0 $. To rewrite it, we need to rearrange the terms in descending order of the power of $ x $: $ 7x^2 + x - 4 = 0 $. Now we can identify the coefficients $ a $, $ b $, and $ c $ for the quadratic formula. $ a = 7 $, $ b = 1 $, and $ c = -4 $.Identifying coefficients: Next, we will use the quadratic formula to find the solutions for $ x $: The quadratic formula is $ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} $. Substitute $ a = 7 $, $ b = 1 $, and $ c = -4 $ into the formula: $ x = \frac{{-(1) \pm \sqrt{{(1)^2 - 4(7)(-4)}}}}{{2(7)}} $.Using the quadratic formula: Now, let's calculate the discriminant, which is the part under the square root in the quadratic formula: $ \sqrt{{b^2 - 4ac}} = \sqrt{{1^2 - 4(7)(-4)}} $. $ \sqrt{{1 + 112}} = \sqrt{{113}} $.Calculating the discriminant: We can now write the solutions using the values we have calculated: $ x = \frac{{-1 \pm \sqrt{{113}}}}{{14}} $. This matches one of the given answer choices, which is (C).

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Solve.

-4+x+7x^(2)=0
Choose 1 answer:
(A)
x=(-7+-sqrt65)/(8)
(B)
x=(-1+-sqrt5)/(2)
(C)
x=(-1+-sqrt113)/(14)
(D)
x=(3+-sqrt21)/(6)

Solve. $\newline$ $-4+x+7 x^{2}=0$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{-7 \pm \sqrt{65}}{8}$ $\newline$ (B) $x=\frac{-1 \pm \sqrt{5}}{2}$ $\newline$ (C) $x=\frac{-1 \pm \sqrt{113}}{14}$ $\newline$ (D) $x=\frac{3 \pm \sqrt{21}}{6}$

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Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

-4+x+7 x^{2}=0

\newline

Choose

1

answer:

\newline

(A)

x=\frac{-7 \pm \sqrt{65}}{8}

\newline

(B)

x=\frac{-1 \pm \sqrt{5}}{2}

\newline

(C)

x=\frac{-1 \pm \sqrt{113}}{14}

\newline

(D)

x=\frac{3 \pm \sqrt{21}}{6}

Rewriting the equation: First, let's rewrite the equation in standard quadratic form, which is $ax^2 + bx + c = 0$ . $\newline$ The given equation is $-4 + x + 7x^2 = 0$ . $\newline$ To rewrite it, we need to rearrange the terms in descending order of the power of $x$ : $\newline$ $7x^2 + x - 4 = 0$ . $\newline$ Now we can identify the coefficients $a$ , $b$ , and $c$ for the quadratic formula. $\newline$ $a = 7$ , $b = 1$ , and $c = -4$ .
Identifying coefficients: Next, we will use the quadratic formula to find the solutions for $x$ : $\newline$ The quadratic formula is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . $\newline$ Substitute $a = 7$ , $b = 1$ , and $c = -4$ into the formula: $\newline$ $x = \frac{{-(1) \pm \sqrt{{(1)^2 - 4(7)(-4)}}}}{{2(7)}}$ .
Using the quadratic formula: Now, let's calculate the discriminant, which is the part under the square root in the quadratic formula: $\newline$ $\sqrt{{b^2 - 4ac}} = \sqrt{{1^2 - 4(7)(-4)}}$ . $\newline$ $\sqrt{{1 + 112}} = \sqrt{{113}}$ .
Calculating the discriminant: We can now write the solutions using the values we have calculated: $\newline$ $x = \frac{{-1 \pm \sqrt{{113}}}}{{14}}$ . $\newline$ This matches one of the given answer choices, which is (C).