Solve. -5x^(2)+7x=-9 Choose 1 answer: (A) x=(5+-sqrt145)/(12) (B) x=1+-sqrt11 (C) x=(-7+-sqrt229)/(-10) (D) x=2,-1

Rewriting the equation: First, we need to rewrite the equation in standard quadratic form, which is ax^2 + bx + c = 0. -5x^2 + 7x = -9 Add 9 to both sides to get the equation in standard form: -5x^2 + 7x + 9 = 0Identifying the coefficients: Now, identify the coefficients a, b, and c from the standard form of the quadratic equation. a = -5 b = 7 c = 9Using the quadratic formula: Next, we will use the quadratic formula to find the solutions for x. The quadratic formula is given by: x = (-b ± sqrt(b^2 - 4ac)) / (2a)Substituting values into the formula: Substitute the values of a, b, and c into the quadratic formula: x = (-(7) ± sqrt((7)^2 - 4(-5)(9))) / (2(-5)) x = (-7 ± sqrt(49 + 180)) / (-10)Simplifying the expression: Simplify the expression under the square root and the denominator: x = (-7 ± sqrt(229)) / (-10)Matching the solution with the choices: Now we have the solutions in the form of the quadratic formula. The expression cannot be simplified further into integers or proper fractions, and it does not match any of the answer choices exactly. However, it is equivalent to one of the choices.Comparing our expression with the given answer choices, we see that it matches choice (C): x = (-7 ± sqrt(229)) / (-10)

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Solve.

-5x^(2)+7x=-9
Choose 1 answer:
(A)
x=(5+-sqrt145)/(12)
(B)
x=1+-sqrt11
(C)
x=(-7+-sqrt229)/(-10)
(D)
x=2,-1

Solve. $\newline$ $-5 x^{2}+7 x=-9$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{5 \pm \sqrt{145}}{12}$ $\newline$ (B) $x=1 \pm \sqrt{11}$ $\newline$ (C) $x=\frac{-7 \pm \sqrt{229}}{-10}$ $\newline$ (D) $x=2,-1$

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Math Problems

Algebra 2

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve.

\newline

-5 x^{2}+7 x=-9

\newline

Choose

1

answer:

\newline

(A)

x=\frac{5 \pm \sqrt{145}}{12}

\newline

(B)

x=1 \pm \sqrt{11}

\newline

(C)

x=\frac{-7 \pm \sqrt{229}}{-10}

\newline

(D)

x=2,-1

Rewriting the equation: First, we need to rewrite the equation in standard quadratic form, which is $ax^2 + bx + c = 0$ . $\newline$ $-5x^2 + 7x = -9$ $\newline$ Add $9$ to both sides to get the equation in standard form: $\newline$ $-5x^2 + 7x + 9 = 0$
Identifying the coefficients: Now, identify the coefficients $a$ , $b$ , and $c$ from the standard form of the quadratic equation. $a = -5$ $b = 7$ $c = 9$
Using the quadratic formula: Next, we will use the quadratic formula to find the solutions for x. The quadratic formula is given by: $\newline$ x = ( $-b \pm \sqrt{b^2 - 4ac}$ ) / ( $2a$ )
Substituting values into the formula: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula: $\newline$ $x = \frac{{-(-7) \pm \sqrt{{(7)^2 - 4(-5)(9)}}}}{{2(-5)}}$ $\newline$ $x = \frac{{-7 \pm \sqrt{{49 + 180}}}}{{-10}}$
Simplifying the expression: Simplify the expression under the square root and the denominator: $\newline$ $x = \frac{{-7 \pm \sqrt{{229}}}}{{-10}}$
Matching the solution with the choices: Now we have the solutions in the form of the quadratic formula. The expression cannot be simplified further into integers or proper fractions, and it does not match any of the answer choices exactly. However, it is equivalent to one of the choices.
Matching the solution with the choices: Now we have the solutions in the form of the quadratic formula. The expression cannot be simplified further into integers or proper fractions, and it does not match any of the answer choices exactly. However, it is equivalent to one of the choices.Comparing our expression with the given answer choices, we see that it matches choice (C): $\newline$ $x = \frac{{-7 \pm \sqrt{229}}}{{-10}}$