Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation(The real numbers system)
x∈/R
Alternative Form
No real solution
Evaluate
x(x×8)=16(x−1)
Remove the parentheses
x×x×8=16(x−1)
Multiply
More Steps
Evaluate
x×x×8
Multiply the terms
x2×8
Use the commutative property to reorder the terms
8x2
8x2=16(x−1)
Expand the expression
More Steps
Evaluate
16(x−1)
Apply the distributive property
16x−16×1
Any expression multiplied by 1 remains the same
16x−16
8x2=16x−16
Move the expression to the left side
8x2−16x+16=0
Substitute a=8,b=−16 and c=16 into the quadratic formula x=2a−b±b2−4ac
x=2×816±(−16)2−4×8×16
Simplify the expression
x=1616±(−16)2−4×8×16
Simplify the expression
More Steps
Evaluate
(−16)2−4×8×16
Multiply the terms
More Steps
Multiply the terms
4×8×16
Multiply the terms
32×16
Multiply the numbers
512
(−16)2−512
Rewrite the expression
162−512
Evaluate the power
256−512
Subtract the numbers
−256
x=1616±−256
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=1−i,x2=1+i
Evaluate
x(x×8)=16(x−1)
Remove the parentheses
x×x×8=16(x−1)
Multiply
More Steps
Evaluate
x×x×8
Multiply the terms
x2×8
Use the commutative property to reorder the terms
8x2
8x2=16(x−1)
Expand the expression
More Steps
Evaluate
16(x−1)
Apply the distributive property
16x−16×1
Any expression multiplied by 1 remains the same
16x−16
8x2=16x−16
Move the expression to the left side
8x2−16x+16=0
Substitute a=8,b=−16 and c=16 into the quadratic formula x=2a−b±b2−4ac
x=2×816±(−16)2−4×8×16
Simplify the expression
x=1616±(−16)2−4×8×16
Simplify the expression
More Steps
Evaluate
(−16)2−4×8×16
Multiply the terms
More Steps
Multiply the terms
4×8×16
Multiply the terms
32×16
Multiply the numbers
512
(−16)2−512
Rewrite the expression
162−512
Evaluate the power
256−512
Subtract the numbers
−256
x=1616±−256
Simplify the radical expression
More Steps
Evaluate
−256
Evaluate the power
256×−1
Evaluate the power
256×i
Evaluate the square root
More Steps
Evaluate
256
Write the number in exponential form with the base of 16
162
Reduce the index of the radical and exponent with 2
16
16i
x=1616±16i
Separate the equation into 2 possible cases
x=1616+16ix=1616−16i
Simplify the expression
More Steps
Evaluate
x=1616+16i
Divide the terms
More Steps
Evaluate
1616+16i
Rewrite the expression
1616(1+i)
Reduce the fraction
1+i
x=1+i
x=1+ix=1616−16i
Simplify the expression
More Steps
Evaluate
x=1616−16i
Divide the terms
More Steps
Evaluate
1616−16i
Rewrite the expression
1616(1−i)
Reduce the fraction
1−i
x=1−i
x=1+ix=1−i
Solution
x1=1−i,x2=1+i
Show Solution
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