Question
Solve the equation(The real numbers system)
x∈/R
Alternative Form
No real solution
Evaluate
4x2×8=8x−4
Multiply the terms
32x2=8x−4
Move the expression to the left side
32x2−8x+4=0
Substitute a=32,b=−8 and c=4 into the quadratic formula x=2a−b±b2−4ac
x=2×328±(−8)2−4×32×4
Simplify the expression
x=648±(−8)2−4×32×4
Simplify the expression
More Steps

Evaluate
(−8)2−4×32×4
Multiply the terms
More Steps

Multiply the terms
4×32×4
Multiply the terms
128×4
Multiply the numbers
512
(−8)2−512
Rewrite the expression
82−512
Evaluate the power
64−512
Subtract the numbers
−448
x=648±−448
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=81−87i,x2=81+87i
Alternative Form
x1≈0.125−0.330719i,x2≈0.125+0.330719i
Evaluate
4x2×8=8x−4
Multiply the terms
32x2=8x−4
Move the expression to the left side
32x2−8x+4=0
Substitute a=32,b=−8 and c=4 into the quadratic formula x=2a−b±b2−4ac
x=2×328±(−8)2−4×32×4
Simplify the expression
x=648±(−8)2−4×32×4
Simplify the expression
More Steps

Evaluate
(−8)2−4×32×4
Multiply the terms
More Steps

Multiply the terms
4×32×4
Multiply the terms
128×4
Multiply the numbers
512
(−8)2−512
Rewrite the expression
82−512
Evaluate the power
64−512
Subtract the numbers
−448
x=648±−448
Simplify the radical expression
More Steps

Evaluate
−448
Evaluate the power
448×−1
Evaluate the power
448×i
Evaluate the power
More Steps

Evaluate
448
Write the expression as a product where the root of one of the factors can be evaluated
64×7
Write the number in exponential form with the base of 8
82×7
The root of a product is equal to the product of the roots of each factor
82×7
Reduce the index of the radical and exponent with 2
87
87×i
x=648±87×i
Separate the equation into 2 possible cases
x=648+87×ix=648−87×i
Simplify the expression
More Steps

Evaluate
x=648+87×i
Divide the terms
More Steps

Evaluate
648+87×i
Rewrite the expression
648(1+7×i)
Cancel out the common factor 8
81+7×i
Simplify
81+87i
x=81+87i
x=81+87ix=648−87×i
Simplify the expression
More Steps

Evaluate
x=648−87×i
Divide the terms
More Steps

Evaluate
648−87×i
Rewrite the expression
648(1−7×i)
Cancel out the common factor 8
81−7×i
Simplify
81−87i
x=81−87i
x=81+87ix=81−87i
Solution
x1=81−87i,x2=81+87i
Alternative Form
x1≈0.125−0.330719i,x2≈0.125+0.330719i
Show Solution
