Question
Simplify the expression
8j4−2j2−16
Evaluate
8j×j3−2j2−16
Solution
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Evaluate
8j×j3
Multiply the terms with the same base by adding their exponents
8j1+3
Add the numbers
8j4
8j4−2j2−16
Show Solution

Factor the expression
2(4j4−j2−8)
Evaluate
8j×j3−2j2−16
Multiply
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Evaluate
8j×j3
Multiply the terms with the same base by adding their exponents
8j1+3
Add the numbers
8j4
8j4−2j2−16
Solution
2(4j4−j2−8)
Show Solution

Find the roots
j1=−42+2129,j2=42+2129
Alternative Form
j1≈−1.242871,j2≈1.242871
Evaluate
8j×j3−2j2−16
To find the roots of the expression,set the expression equal to 0
8j×j3−2j2−16=0
Multiply
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Multiply the terms
8j×j3
Multiply the terms with the same base by adding their exponents
8j1+3
Add the numbers
8j4
8j4−2j2−16=0
Solve the equation using substitution t=j2
8t2−2t−16=0
Substitute a=8,b=−2 and c=−16 into the quadratic formula t=2a−b±b2−4ac
t=2×82±(−2)2−4×8(−16)
Simplify the expression
t=162±(−2)2−4×8(−16)
Simplify the expression
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Evaluate
(−2)2−4×8(−16)
Multiply
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Multiply the terms
4×8(−16)
Rewrite the expression
−4×8×16
Multiply the terms
−512
(−2)2−(−512)
Rewrite the expression
22−(−512)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+512
Evaluate the power
4+512
Add the numbers
516
t=162±516
Simplify the radical expression
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Evaluate
516
Write the expression as a product where the root of one of the factors can be evaluated
4×129
Write the number in exponential form with the base of 2
22×129
The root of a product is equal to the product of the roots of each factor
22×129
Reduce the index of the radical and exponent with 2
2129
t=162±2129
Separate the equation into 2 possible cases
t=162+2129t=162−2129
Simplify the expression
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Evaluate
t=162+2129
Divide the terms
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Evaluate
162+2129
Rewrite the expression
162(1+129)
Cancel out the common factor 2
81+129
t=81+129
t=81+129t=162−2129
Simplify the expression
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Evaluate
t=162−2129
Divide the terms
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Evaluate
162−2129
Rewrite the expression
162(1−129)
Cancel out the common factor 2
81−129
t=81−129
t=81+129t=81−129
Substitute back
j2=81+129j2=81−129
Solve the equation for j
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Substitute back
j2=81+129
Take the root of both sides of the equation and remember to use both positive and negative roots
j=±81+129
Simplify the expression
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Evaluate
81+129
To take a root of a fraction,take the root of the numerator and denominator separately
81+129
Simplify the radical expression
221+129
Multiply by the Conjugate
22×21+129×2
Multiply the numbers
22×22+2129
Multiply the numbers
42+2129
j=±42+2129
Separate the equation into 2 possible cases
j=42+2129j=−42+2129
j=42+2129j=−42+2129j2=81−129
Solve the equation for j
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Substitute back
j2=81−129
Take the root of both sides of the equation and remember to use both positive and negative roots
j=±81−129
Simplify the expression
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Evaluate
81−129
Evaluate the power
8129−1×−1
Evaluate the power
8129−1×i
Evaluate the power
42129−2i
j=±42129−2i
Separate the equation into 2 possible cases
j=42129−2ij=−42129−2i
j=42+2129j=−42+2129j=42129−2ij=−42129−2i
Calculate
j=42+2129j=−42+2129
Solution
j1=−42+2129,j2=42+2129
Alternative Form
j1≈−1.242871,j2≈1.242871
Show Solution
