X^2=-4-4600*0.1*(X+2) — step-by-step solution

1) Let's solve in

ℝ

X^{2} = - 4 - 4600 \cdot 0.1 \cdot (X + 2)

X^{2} = - 4 - 460 \cdot (X + 2)

X^{2} + 4 + 460 \cdot (X + 2) = 0

X^{2} + 4 + (460 X + 920) = 0

X^{2} + 924 + 460 X = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = 460^{2} - 4 \cdot 1 \cdot 924

Δ = 211600 - 4 \cdot 924

Δ = 211600 - 3696

Δ = 207904

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

X1 = \frac{- 460 - \sqrt{207904}}{2}

X1 = - \frac{460 + 4 \cdot \sqrt{12994}}{2}

X1 = - (230 + 2 \cdot \sqrt{12994})

X1 = - 230 - 2 \cdot \sqrt{12994}

For the second solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

X2 = \frac{- 460 + \sqrt{207904}}{2}

X2 = \frac{- 460 + 4 \cdot \sqrt{12994}}{2}

X2 = - 230 + 2 \cdot \sqrt{12994}

Solution found:

X = - 2 \cdot \sqrt{12994} - 230

Solution found:

X = 2 \cdot \sqrt{12994} - 230

▶Solution:

X = {- 2 \cdot \sqrt{12994} - 230, 2 \cdot \sqrt{12994} - 230}

2) The numeric value of:

X = {- 2 \cdot \sqrt{12994} - 230, 2 \cdot \sqrt{12994} - 230}

equals:

X = {- 2 \cdot \approx 113.9912 - 230, 2 \cdot \approx 113.9912 - 230}

X = {- \approx 227.9825 - 230, \approx 227.9825 - 230}

▷

X = {\approx -457.9825, \approx -2.0175}