x^2-2x=2 — step-by-step solution

1) Let's solve in

ℝ

x^{2} - 2 x = 2

x^{2} - 2 x - 2 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-2)}^{2} - 4 \cdot 1 \cdot (-2)

Δ = 4 - 4 \cdot (-2)

Δ = 4 + 8

Δ = 12

Since

Δ > 0

, the equation has two solutions:

The first solution is:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{2 - \sqrt{12}}{2}

x1 = \frac{2 - 2 \cdot \sqrt{3}}{2}

x1 = 1 - \sqrt{3}

The second solution is:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{2 + \sqrt{12}}{2}

x2 = \frac{2 + 2 \cdot \sqrt{3}}{2}

x2 = 1 + \sqrt{3}

Solution obtained:

x = 1 - \sqrt{3}

Solution obtained:

x = \sqrt{3} + 1

▶Solution:

x = {1 - \sqrt{3}, \sqrt{3} + 1}

2) The numeric value of:

x = {1 - \sqrt{3}, \sqrt{3} + 1}

is:

x = {1 - \approx 1.7321, \approx 1.7321 + 1}

▷

x = {\approx -0.7321, \approx 2.7321}