Question

using the quadratic formula to solve (2x^2 = 4x - 7), what are the values of (x)?

\\(2 \pm \sqrt{10}i\\)
\\(1 \pm \sqrt{10}i\\)
\\(\frac{2 \pm \sqrt{10}i}{2}\\)
\\(1 \pm \sqrt{5}i\\)

Explanation:

Rearrange equation to standard form

Using the Quadratic Formula knowledge point

$$
LATEXBLOCK0
$$

Identify coefficients

Using the Quadratic Formula knowledge point

$$ a = 2, \quad b = -4, \quad c = 7 $$

Apply the quadratic formula

Using the Quadratic Formula knowledge point

$$
LATEXBLOCK1
$$

Simplify the radical expression

Using the Complex Roots knowledge point

$$
LATEXBLOCK2
$$

Simplify the fraction

Using the Complex Roots knowledge point

$$
LATEXBLOCK3
$$

Answer:

• (A) \(2 \pm \sqrt{10}i\)
• (B) \(1 \pm \sqrt{10}i\)
• (C) \(\frac{2 \pm \sqrt{10}i}{2}\) (Correct answer)
• (D) \(1 \pm \sqrt{5}i\)