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)

Write equation in standard form: Write the equation in standard form. To solve the quadratic equation using the quadratic formula, we need to write the equation in the standard form ax^2 + bx + c = 0. We start by moving all terms to one side of the equation. 10x^2 - 9x - 6 = 0 Here, a = 10, b = -9, and c = -6.Apply quadratic formula: Apply the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). We will substitute the values of a, b, and c into the formula. x = (9 ± √((-9)^2 - 4*10*(-6))) / (2*10)Calculate discriminant: Calculate the discriminant. The discriminant is the part of the quadratic formula under the square root, b^2 - 4ac. Discriminant = (-9)^2 - 4*10*(-6) Discriminant = 81 + 240 Discriminant = 321Substitute discriminant into formula: Substitute the discriminant back into the formula. Now that we have the discriminant, we can substitute it back into the quadratic formula. x = (9 ± √321) / (2*10) x = (9 ± √321) / 20Simplify solutions: Simplify the solutions. We have two possible solutions for x, corresponding to the '±' in the formula. x = (9 + √321) / 20 or x = (9 - √321) / 20 These are the solutions in their simplest radical form.

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

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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}

Write equation in standard form: Write the equation in standard form. $\newline$ To solve the quadratic equation using the quadratic formula, we need to write the equation in the standard form $ax^2 + bx + c = 0$ . We start by moving all terms to one side of the equation. $\newline$ $10x^2 - 9x - 6 = 0$ $\newline$ Here, $a = 10$ , $b = -9$ , and $c = -6$ .
Apply quadratic formula: Apply the quadratic formula. $\newline$ The quadratic formula is $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ . We will 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: Calculate the discriminant. $\newline$ The discriminant is the part of the quadratic formula under the square root, $b^2 - 4ac$ . $\newline$ Discriminant = $(-9)^2 - 4 \cdot 10 \cdot (-6)$ $\newline$ Discriminant = $81 + 240$ $\newline$ Discriminant = $321$
Substitute discriminant into formula: Substitute the discriminant back into the formula. $\newline$ Now that we have the discriminant, we can substitute it back into the quadratic formula. $\newline$ $x = \frac{9 \pm \sqrt{321}}{2 \cdot 10}$ $\newline$ $x = \frac{9 \pm \sqrt{321}}{20}$
Simplify solutions: Simplify the solutions. $\newline$ We have two possible solutions for x, corresponding to the ' $\pm$ ' in the formula. $\newline$ $x = (9 + \sqrt{321}) / 20$ or $x = (9 - \sqrt{321}) / 20$ $\newline$ These are the solutions in their simplest radical form.