ssignment
Question 35, 3.3.69
HW Score: 48.75%, 23.89

Solve the equation.

(Use a comma to separate answers as needed. Type an exact answer, using radicals and as needed.)

Ask by Zimmerman Romero. in the United States

Mar 14,2025

Question

ssignment
Question 35, 3.3.69
HW Score: 48.75%, 23.89

Solve the equation.

(Use a comma to separate answers as needed. Type an exact answer, using radicals and as needed.)

Ask by Zimmerman Romero. in the United States

Mar 14,2025

UpStudy AI · Accepted Answer

We start with the equation
$$
3x^2 + 5 = 7x.
$$
Subtract $$7x$$ from both sides to obtain the standard quadratic form:
$$
3x^2 - 7x + 5 = 0.
$$

Now, we apply the quadratic formula:
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a},
$$
with $$a = 3$$, $$b = -7$$, and $$c = 5$$.

First, compute the discriminant:
$$
b^2 - 4ac = (-7)^2 - 4(3)(5) = 49 - 60 = -11.
$$

Since the discriminant is negative, the solutions will involve imaginary numbers. Substitute the values into the quadratic formula:
$$
x = \frac{-(-7) \pm \sqrt{-11}}{2 \cdot 3} = \frac{7 \pm \sqrt{-11}}{6}.
$$

Recall that $$\sqrt{-11} = i\sqrt{11}$$. Therefore, the solutions are:
$$
x = \frac{7 \pm i\sqrt{11}}{6}.
$$

Thus, the final answer is:
$$
\boxed{\frac{7 \pm i\sqrt{11}}{6}}.
$$
The solutions are $$ x = \frac{7 + i\sqrt{11}}{6} $$ and $$ x = \frac{7 - i\sqrt{11}}{6} $$.

ssignment
Question 35, 3.3.69
HW Score: 48.75%, 23.89

Solve the equation.

(Use a comma to separate answers as needed. Type an exact answer, using radicals and as needed.)

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Solución

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ssignment Question 35, 3.3.69 HW Score: 48.75%, 23.89 Solve the equation. (Use a comma to separate answers as needed. Type an exact answer, using radicals and as needed.)

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Solución

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ssignment
Question 35, 3.3.69
HW Score: 48.75%, 23.89

Solve the equation.

(Use a comma to separate answers as needed. Type an exact answer, using radicals and as needed.)