x^2+10x+42=-3x — step-by-step solution

Let's solve in

ℝ

x^{2} + 10 x + 42 = -3 x

x^{2}

+ 10 x

+ 42

+ 3 x = 0

x^{2} + 13 x + 42 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = 13^{2} - 4 \cdot 1 \cdot 42

Δ = 169 - 4 \cdot 42

Δ = 169 - 168

Δ = 1

Since

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{- 13 - 1}{2}

x1 = - \frac{14}{2}

x1 = -7

Solution second:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{- 13 + 1}{2}

x2 = - \frac{12}{2}

x2 = -6

Solution found:

x = -7

Solution obtained:

x = -6

▶Solution:

x = {-7, -6}