2x^2+5x-1=0 — step-by-step solution

⚠ 2x is read as the product 2*x: for a power, write 2^x

⚠ 5x is read as the product 5*x: for a power, write 5^x

1) Let's solve in

ℝ

2 x^{2} + 5 x - 1 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = 5^{2} - 4 \cdot 2 \cdot (-1)

ℹ

5^{2}

25

‖

4 \cdot 2

8

‖

- 8 \cdot (-1)

8

Δ = 25 + 8

Δ = 33

Δ > 0

, the equation has two solutions:

The first solution is:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{- 5 - \sqrt{33}}{2 \cdot 2}

x1 = - \frac{5 + \sqrt{33}}{4}

The second solution is:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{- 5 + \sqrt{33}}{2 \cdot 2}

x2 = \frac{- 5 + \sqrt{33}}{4}

Solution found:

x = - \frac{\sqrt{33} + 5}{4}

Solution obtained:

x = \frac{\sqrt{33} - 5}{4}

▶Solution:

x = {- \frac{\sqrt{33} + 5}{4}, \frac{\sqrt{33} - 5}{4}}

2) The numeric value of:

x = {- \frac{\sqrt{33} + 5}{4}, \frac{\sqrt{33} - 5}{4}}

equals:

x = {- \frac{\approx 5.7446 + 5}{4}, \frac{\approx 5.7446 - 5}{4}}

x = {- \frac{\approx 10.7446}{4}, \frac{\approx 0.7446}{4}}

▷

x = {\approx -2.6861, \approx 0.1861}