Solve. 8x+10x^(2)-6=17 x Choose 1 answer: (A) x=(3)/(4),1 (B) x=(4+-sqrt26)/(10) (C) x=(-1+-sqrt109)/(18) (D) x=(9+-sqrt321)/(20)

Rearrange the equation: First, we need to rearrange the equation into standard quadratic form, ax^2 + bx + c = 0. The given equation is 8x + 10x^2 - 6 = 17x. Subtract 17x from both sides to get 10x^2 - 9x - 6 = 0.Identify the coefficients: Now, identify the coefficients a, b, and c from the quadratic equation 10x^2 - 9x - 6 = 0. Here, a = 10, b = -9, and c = -6.Use the quadratic formula: Next, we will use the quadratic formula to find the solutions for x, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). Substitute a = 10, b = -9, and c = -6 into the formula.Calculate the discriminant: Now, calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. Discriminant = (-9)^2 - 4(10)(-6) = 81 + 240 = 321.Find the solutions for x: With the discriminant calculated, we can now find the two solutions for x. x = [9 ± sqrt(321)] / (2*10).Simplify the solutions: Simplify the solutions for x. x = (9 ± sqrt(321)) / 20.Choose the correct answer: The solutions are in the form that matches one of the answer choices provided. The correct answer choice is (D) x = (9 ± sqrt(321)) / 20.

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8x+10x^(2)-6=17 x
Choose 1 answer:
(A)
x=(3)/(4),1
(B)
x=(4+-sqrt26)/(10)
(C)
x=(-1+-sqrt109)/(18)
(D)
x=(9+-sqrt321)/(20)

Solve. $\newline$ $8 x+10 x^{2}-6=17 x$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{3}{4}, 1$ $\newline$ (B) $x=\frac{4 \pm \sqrt{26}}{10}$ $\newline$ (C) $x=\frac{-1 \pm \sqrt{109}}{18}$ $\newline$ (D) $x=\frac{9 \pm \sqrt{321}}{20}$

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Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

8 x+10 x^{2}-6=17 x

\newline

Choose

1

answer:

\newline

(A)

x=\frac{3}{4}, 1

\newline

(B)

x=\frac{4 \pm \sqrt{26}}{10}

\newline

(C)

x=\frac{-1 \pm \sqrt{109}}{18}

\newline

(D)

x=\frac{9 \pm \sqrt{321}}{20}

Rearrange the equation: First, we need to rearrange the equation into standard quadratic form, $ax^2 + bx + c = 0$ . $\newline$ The given equation is $8x + 10x^2 - 6 = 17x$ . $\newline$ Subtract $17x$ from both sides to get $10x^2 - 9x - 6 = 0$ .
Identify the coefficients: Now, identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation $10x^2 - 9x - 6 = 0$ . $\newline$ Here, $a = 10$ , $b = -9$ , and $c = -6$ .
Use the quadratic formula: Next, we will use the quadratic formula to find the solutions for x, which is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . Substitute $a = 10$ , $b = -9$ , and $c = -6$ into the formula.
Calculate the discriminant: Now, calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . $\newline$ Discriminant = $(-9)^2 - 4(10)(-6) = 81 + 240 = 321$ .
Find the solutions for $x$ : With the discriminant calculated, we can now find the two solutions for $x$ . $\newline$ $x = \frac{{$ $9$ \pm \sqrt{ $321$ }}}{{ $2$ \cdot $10$ }}.
Simplify the solutions: Simplify the solutions for $x$ . $x = \frac{{9 \pm \sqrt{{321}}}}{20}.$
Choose the correct answer: The solutions are in the form that matches one of the answer choices provided. $\newline$ The correct answer choice is (D) $x = \frac{9 \pm \sqrt{321}}{20}$ .