r^2-6r+34=0 — step-by-step solution

Let's solve in

ℝ

r^{2} - 6 r + 34 = 0

Given the quadratic form

a r^{2} + b r + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 1

b = -6

and

c = 34

Δ = {(-6)}^{2} - 4 \cdot 1 \cdot 34

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

{(-6)}^{2}

(-6) \cdot (-6)

36

Δ = 36 - 4 \cdot 34

ⓘ Multiplications are done before additions and subtractions:

4 \cdot 34

4 \cdot (30 + 4)

4 \cdot 30 + 4 \cdot 4

120 + 16

136

Δ = 36 - 136

ⓘ Start from

36

and move back

136

on the number line, going below zero:

36 - 136

-100

Δ = -100

Δ < 0

, the equation has no real root.

▶Solution:

r \in \emptyset