Solve. 3x=9x^(2)-10 Choose 1 answer: (A) x=(7+-sqrt77)/(2) (B) x=(-2+-sqrt13)/(-3) (C) x=(-5+-sqrt305)/(14) (D) x=(-1+-sqrt41)/(-6)

Move terms to one side: Write the equation in standard form by moving all terms to one side. We want to get the equation into the form ax^2 + bx + c = 0. 3x = 9x^2 - 10 0 = 9x^2 - 3x - 10 What are the values of a, b, and c? a = 9, b = -3, c = -10Write equation in standard form: Use the quadratic formula to solve for x. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Substitute a = 9, b = -3, and c = -10 into the quadratic formula. x = (-(-3) ± sqrt((-3)^2 - 4*9*(-10))) / (2*9)Values of a, b, and c: Simplify the equation. x = (3 ± sqrt(9 + 360)) / 18 x = (3 ± sqrt(369)) / 18Use quadratic formula: Calculate the discriminant (the value inside the square root). sqrt(369) is the discriminant.Substitute values into formula: Find the two possible solutions for x. x = (3 + sqrt(369)) / 18 or x = (3 - sqrt(369)) / 18Simplify equation: Simplify the square root. sqrt(369) is approximately 19.21. x = (3 + 19.21) / 18 or x = (3 - 19.21) / 18Calculate discriminant: Calculate the two solutions. x ≈ (3 + 19.21) / 18 or x ≈ (3 - 19.21) / 18 x ≈ 22.21 / 18 or x ≈ -16.21 / 18 x ≈ 1.23 or x ≈ -0.90Find possible solutions: Check the solutions against the answer choices. None of the answer choices match the solutions we found.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve.

3x=9x^(2)-10
Choose 1 answer:
(A)
x=(7+-sqrt77)/(2)
(B)
x=(-2+-sqrt13)/(-3)
(C)
x=(-5+-sqrt305)/(14)
(D)
x=(-1+-sqrt41)/(-6)

Solve. $\newline$ $3 x=9 x^{2}-10$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{7 \pm \sqrt{77}}{2}$ $\newline$ (B) $x=\frac{-2 \pm \sqrt{13}}{-3}$ $\newline$ (ᄃ) $x=\frac{-5 \pm \sqrt{305}}{14}$ $\newline$ (D) $x=\frac{-1 \pm \sqrt{41}}{-6}$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

3 x=9 x^{2}-10

\newline

Choose

1

answer:

\newline

(A)

x=\frac{7 \pm \sqrt{77}}{2}

\newline

(B)

x=\frac{-2 \pm \sqrt{13}}{-3}

\newline

(ᄃ)

x=\frac{-5 \pm \sqrt{305}}{14}

\newline

(D)

x=\frac{-1 \pm \sqrt{41}}{-6}

Move terms to one side: Write the equation in standard form by moving all terms to one side. $\newline$ We want to get the equation into the form $ax^2 + bx + c = 0$ . $\newline$ $3x = 9x^2 - 10$ $\newline$ $0 = 9x^2 - 3x - 10$ $\newline$ What are the values of $a$ , $b$ , and $c$ ? $\newline$ $a = 9$ , $b = -3$ , $c = -10$
Write equation in standard form: Use the quadratic formula to solve for $x$ . $\newline$ The quadratic formula is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . $\newline$ Substitute $a = 9$ , $b = -3$ , and $c = -10$ into the quadratic formula. $\newline$ $x = \frac{{-(-3) \pm \sqrt{{(-3)^2 - 4 \cdot 9 \cdot (-10)}}}}{{2 \cdot 9}}$
Values of $a$ , $b$ , and $c$ : Simplify the equation. $x = \frac{3 \pm \sqrt{9 + 360}}{18}$ $x = \frac{3 \pm \sqrt{369}}{18}$
Use quadratic formula: Calculate the discriminant (the value inside the square root). $\sqrt{369}$ is the discriminant.
Substitute values into formula: Find the two possible solutions for $x$ . $x = \frac{3 + \sqrt{369}}{18}$ or $x = \frac{3 - \sqrt{369}}{18}$
Simplify equation: Simplify the square root. $\sqrt{369}$ is approximately $19.21$ . $x = \frac{3 + 19.21}{18}$ or $x = \frac{3 - 19.21}{18}$
Calculate discriminant: Calculate the two solutions. $\newline$ $x \approx (3 + 19.21) / 18$ or $x \approx (3 - 19.21) / 18$ $\newline$ $x \approx 22.21 / 18$ or $x \approx -16.21 / 18$ $\newline$ $x \approx 1.23$ or $x \approx -0.90$
Find possible solutions: Check the solutions against the answer choices. $\newline$ None of the answer choices match the solutions we found.