Solve the equation using the quadratic formula.

The solution set is { }.
(Simplify your answer. Type an exact answer, using radicals and as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers
as needed.)

Ask by Rodriguez Chan. in the United States

Mar 15,2025

Question

Solve the equation using the quadratic formula.

The solution set is { }.
(Simplify your answer. Type an exact answer, using radicals and as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers
as needed.)

Ask by Rodriguez Chan. in the United States

Mar 15,2025

UpStudy AI · Accepted Answer

We start with the quadratic equation
$$
x^2 - 2x + 26 = 0.
$$
The quadratic formula is
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
$$
Here, $$ a = 1 $$, $$ b = -2 $$, and $$ c = 26 $$.

Substitute these values into the formula:
$$
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(26)}}{2(1)}.
$$

Simplify step by step:
1. Compute $$-(-2)$$:
$$
-(-2) = 2.
$$

2. Compute the discriminant $$b^2 - 4ac$$:
$$
(-2)^2 - 4(1)(26) = 4 - 104 = -100.
$$

3. Substitute the discriminant back into the formula:
$$
x = \frac{2 \pm \sqrt{-100}}{2}.
$$

4. Simplify $$\sqrt{-100}$$ using $$ i $$:
$$
\sqrt{-100} = 10i.
$$

5. Write the expression for $$x$$:
$$
x = \frac{2 \pm 10i}{2}.
$$

6. Divide numerator by 2:
$$
x = 1 \pm 5i.
$$

Thus, the solution set is $$\{1 + 5i,\, 1 - 5i\}$$.
The solutions are $$ x = 1 + 5i $$ and $$ x = 1 - 5i $$.

Solve the equation using the quadratic formula.

The solution set is { }.
(Simplify your answer. Type an exact answer, using radicals and as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers
as needed.)

Upstudy AI Solution

Answer

Solution

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Solve the equation using the quadratic formula. The solution set is { }. (Simplify your answer. Type an exact answer, using radicals and as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Upstudy AI Solution

Answer

Solution

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Latest Algebra Questions

Solve the equation using the quadratic formula.

The solution set is { }.
(Simplify your answer. Type an exact answer, using radicals and as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers
as needed.)