Question

Which are the solutions of the quadratic equation?

x2 = 7x + 4

StartFraction negative 7 minus StartRoot 65 EndRoot Over 2 EndFraction comma StartFraction negative 7 + StartRoot 65 EndRoot Over 2 EndFraction
–7, 0
StartFraction 7 minus StartRoot 65 EndRoot Over 2 EndFraction comma StartFraction 7 + StartRoot 65 EndRoot Over 2 EndFraction
7, 0

Answer 1

x₁ = -0.531

x₂ = 7.531

Explanation:

x² = 7x + 4

x² - 7x - 4 = 0

x = {-(-7)±√((-7)²-(4*1*-4))} / (2*1)

x = {7±√(49+16)} / 2

x = {7±√65} / 2

x = {7±8.062} / 2

x₁ = {7-8.062} / 2 = -1,062/2 = -0.531

x₂ = {7+8.062}/2 = 15.062/2 = 7.531

Comprobación:

x₁

-0.531² = 7*-0.531 + 4

0.2821 = -3.7129 + 4

x₂

7.531² = 7*7.531 + 4

56.7179 = 52.7179 + 4