MATH SOLVE

2 months ago

Q:
# Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 β 4x = 5

Accepted Solution

A:

Solve for x over the real numbers:

x^2 - 4 x = 5

Subtract 5 from both sides:

x^2 - 4 x - 5 = 0

x = (4 Β± sqrt((-4)^2 - 4 (-5)))/2 = (4 Β± sqrt(16 + 20))/2 = (4 Β± sqrt(36))/2:

x = (4 + sqrt(36))/2 or x = (4 - sqrt(36))/2

sqrt(36) = sqrt(4Γ9) = sqrt(2^2Γ3^2) = 2Γ3 = 6:

x = (4 + 6)/2 or x = (4 - 6)/2

(4 + 6)/2 = 10/2 = 5:

x = 5 or x = (4 - 6)/2

(4 - 6)/2 = -2/2 = -1:

Answer:Β x = 5 or x = -1

x^2 - 4 x = 5

Subtract 5 from both sides:

x^2 - 4 x - 5 = 0

x = (4 Β± sqrt((-4)^2 - 4 (-5)))/2 = (4 Β± sqrt(16 + 20))/2 = (4 Β± sqrt(36))/2:

x = (4 + sqrt(36))/2 or x = (4 - sqrt(36))/2

sqrt(36) = sqrt(4Γ9) = sqrt(2^2Γ3^2) = 2Γ3 = 6:

x = (4 + 6)/2 or x = (4 - 6)/2

(4 + 6)/2 = 10/2 = 5:

x = 5 or x = (4 - 6)/2

(4 - 6)/2 = -2/2 = -1:

Answer:Β x = 5 or x = -1