Question

using the quadratic formula to solve (x^2 = 5 - x), what are the values of (x)?

\\(\circ\\) \\(\frac{-1 \pm \sqrt{21}}{2}\\)

\\(\circ\\) \\(\frac{-1 \pm \sqrt{19}i}{2}\\)

\\(\circ\\) \\(\frac{5 \pm \sqrt{21}}{2}\\)

\\(\circ\\) \\(\frac{1 \pm \sqrt{19}i}{2}\\)

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Rewrite in standard form

$$ x^2 + x - 5 = 0 $$

Step 2: Identify coefficients

$$ a = 1, \quad b = 1, \quad c = -5 $$

Step 3: Apply the quadratic formula

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

$$ x = \frac{-1 \pm \sqrt{1^2 - 4(1)(-5)}}{2(1)} $$

$$ x = \frac{-1 \pm \sqrt{1 + 20}}{2} $$

$$ x = \frac{-1 \pm \sqrt{21}}{2} $$

Answer:

$$ \frac{-1 \pm \sqrt{21}}{2} $$