Question
Solve the equation(The real numbers system)
x∈/R
Alternative Form
No real solution
Evaluate
−4=6x2×2−4x
Multiply the terms
−4=12x2−4x
Swap the sides
12x2−4x=−4
Move the expression to the left side
12x2−4x+4=0
Substitute a=12,b=−4 and c=4 into the quadratic formula x=2a−b±b2−4ac
x=2×124±(−4)2−4×12×4
Simplify the expression
x=244±(−4)2−4×12×4
Simplify the expression
More Steps

Evaluate
(−4)2−4×12×4
Multiply the terms
More Steps

Multiply the terms
4×12×4
Multiply the terms
48×4
Multiply the numbers
192
(−4)2−192
Rewrite the expression
42−192
Evaluate the power
16−192
Subtract the numbers
−176
x=244±−176
Solution
x∈/R
Alternative Form
No real solution
Show Solution

Solve the equation(The complex numbers system)
Solve using the quadratic formula in the complex numbers system
Solve by completing the square in the complex numbers system
Solve using the PQ formula in the complex numbers system
x1=61−611i,x2=61+611i
Alternative Form
x1≈0.16˙−0.552771i,x2≈0.16˙+0.552771i
Evaluate
−4=6x2×2−4x
Multiply the terms
−4=12x2−4x
Swap the sides
12x2−4x=−4
Move the expression to the left side
12x2−4x+4=0
Substitute a=12,b=−4 and c=4 into the quadratic formula x=2a−b±b2−4ac
x=2×124±(−4)2−4×12×4
Simplify the expression
x=244±(−4)2−4×12×4
Simplify the expression
More Steps

Evaluate
(−4)2−4×12×4
Multiply the terms
More Steps

Multiply the terms
4×12×4
Multiply the terms
48×4
Multiply the numbers
192
(−4)2−192
Rewrite the expression
42−192
Evaluate the power
16−192
Subtract the numbers
−176
x=244±−176
Simplify the radical expression
More Steps

Evaluate
−176
Evaluate the power
176×−1
Evaluate the power
176×i
Evaluate the power
More Steps

Evaluate
176
Write the expression as a product where the root of one of the factors can be evaluated
16×11
Write the number in exponential form with the base of 4
42×11
The root of a product is equal to the product of the roots of each factor
42×11
Reduce the index of the radical and exponent with 2
411
411×i
x=244±411×i
Separate the equation into 2 possible cases
x=244+411×ix=244−411×i
Simplify the expression
More Steps

Evaluate
x=244+411×i
Divide the terms
More Steps

Evaluate
244+411×i
Rewrite the expression
244(1+11×i)
Cancel out the common factor 4
61+11×i
Simplify
61+611i
x=61+611i
x=61+611ix=244−411×i
Simplify the expression
More Steps

Evaluate
x=244−411×i
Divide the terms
More Steps

Evaluate
244−411×i
Rewrite the expression
244(1−11×i)
Cancel out the common factor 4
61−11×i
Simplify
61−611i
x=61−611i
x=61+611ix=61−611i
Solution
x1=61−611i,x2=61+611i
Alternative Form
x1≈0.16˙−0.552771i,x2≈0.16˙+0.552771i
Show Solution
