-2x^2+4x-2=0 — step-by-step solution

Let's solve in

ℝ

- 2 x^{2} + 4 x - 2 = 0

Since

-2 \neq 0

, divide both sides by

-2

x^{2} - 2 x + 1 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 1

b = -2

and

c = 1

Δ = {(-2)}^{2} - 4 \cdot 1 \cdot 1

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{(-2)}^{2}

(-2) \cdot (-2)

4

Δ = 4 - 4

ⓘ Start from

4

and move back

4

on the number line, down to zero:

4 - 4

0

Δ = 0

Δ = 0

, the equation has one root:

The quadratic formula gives

x_{0}

- \frac{b}{2 a}

\frac{- (-2)}{2 \cdot 1}

x_{0} = \frac{2}{2}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{2}{2}

1

x_{0} = 1

▶Solution obtained:

x = 1