Solve. 10x^(2)=6+9x Choose 1 answer: (A) x=(5+-sqrt65)/(-2) (B) x=(9+-sqrt321)/(20) (c) x=(4+-sqrt26)/(10) (D) x=(-1+-sqrt109)/(18)

Rewrite equation in standard form: First, we need to rewrite the equation in standard quadratic form, ax^2 + bx + c = 0. 10x^2 - 9x - 6 = 0Identify coefficients: Identify the coefficients a, b, and c to use in the quadratic formula. In this equation, a = 10, b = -9, and c = -6.Apply quadratic formula: The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Substitute the values of a, b, and c into the formula. x = (-(-9) ± sqrt((-9)^2 - 4*10*(-6))) / (2*10)Calculate discriminant: Simplify the equation by calculating the discriminant (the part under the square root). Discriminant = (-9)^2 - 4*10*(-6) = 81 + 240 = 321Insert discriminant into formula: Now, insert the discriminant back into the quadratic formula. x = (9 ± sqrt(321)) / 20Solve for x: The solutions to the equation are therefore: x = (9 + sqrt(321)) / 20 and x = (9 - sqrt(321)) / 20

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve.

10x^(2)=6+9x
Choose 1 answer:
(A)
x=(5+-sqrt65)/(-2)
(B)
x=(9+-sqrt321)/(20)
(c)
x=(4+-sqrt26)/(10)
(D)
x=(-1+-sqrt109)/(18)

Solve. $\newline$ $10x^{2}=6+9x$ $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $x=\frac{5\pm\sqrt{65}}{-2}$ $\newline$ (B) $\newline$ $x=\frac{9\pm\sqrt{321}}{20}$ $\newline$ (C) $\newline$ $x=\frac{4\pm\sqrt{26}}{10}$ $\newline$ (D) $\newline$ $x=\frac{-1\pm\sqrt{109}}{18}$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

10x^{2}=6+9x

\newline

Choose

1

answer:

\newline

(A)

\newline

x=\frac{5\pm\sqrt{65}}{-2}

\newline

(B)

\newline

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

\newline

(C)

\newline

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

\newline

(D)

\newline

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

Rewrite equation in standard form: First, we need to rewrite the equation in standard quadratic form, $ax^2 + bx + c = 0$ . $\newline$ $10x^2 - 9x - 6 = 0$
Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ to use in the quadratic formula. In this equation, $a = 10$ , $b = -9$ , and $c = -6$ .
Apply quadratic formula: The quadratic formula is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . Substitute the values of $a$ , $b$ , and $c$ into the formula. $\newline$ $x = \frac{{-(-9) \pm \sqrt{{(-9)^2 - 4 \cdot 10 \cdot (-6)}}}}{{2 \cdot 10}}$
Calculate discriminant: Simplify the equation by calculating the discriminant (the part under the square root). $\newline$ Discriminant = $(-9)^2 - 4 \cdot 10 \cdot (-6) = 81 + 240 = 321$
Insert discriminant into formula: Now, insert the discriminant back into the quadratic formula. $x = \frac{{9 \pm \sqrt{{321}}}}{20}$
Solve for x: The solutions to the equation are therefore: $\newline$ x = $(\frac{9 + \sqrt{321}}{20})$ and x = $(\frac{9 - \sqrt{321}}{20})$