Algebra
Calculus
Trigonometry
Matrix
Question
x−4(x−2)x×x
Simplify the expression
x−4x3+8x2
Evaluate
x−4(x−2)x×x
Multiply
More Steps
Multiply the terms
4(x−2)x×x
Multiply the terms
4(x−2)x2
Multiply the terms
4x2(x−2)
x−4x2(x−2)
Solution
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Evaluate
−4x2(x−2)
Apply the distributive property
−4x2×x−(−4x2×2)
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
−4x3−(−4x2×2)
Multiply the numbers
−4x3−(−8x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−4x3+8x2
x−4x3+8x2
Show Solution
Factor the expression
x(1−4x2+8x)
Evaluate
x−4(x−2)x×x
Multiply
More Steps
Evaluate
4(x−2)x×x
Multiply the terms
4(x−2)x2
Multiply the terms
4x2(x−2)
x−4x2(x−2)
Rewrite the expression
x−x×4x(x−2)
Factor out x from the expression
x(1−4x(x−2))
Solution
x(1−4x2+8x)
Show Solution
Find the roots
x1=22−5,x2=0,x3=22+5
Alternative Form
x1≈−0.118034,x2=0,x3≈2.118034
Evaluate
x−4(x−2)x×x
To find the roots of the expression,set the expression equal to 0
x−4(x−2)x×x=0
Multiply
More Steps
Multiply the terms
4(x−2)x×x
Multiply the terms
4(x−2)x2
Multiply the terms
4x2(x−2)
x−4x2(x−2)=0
Calculate
More Steps
Evaluate
−4x2(x−2)
Apply the distributive property
−4x2×x−(−4x2×2)
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
−4x3−(−4x2×2)
Multiply the numbers
−4x3−(−8x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−4x3+8x2
x−4x3+8x2=0
Factor the expression
x(1−4x2+8x)=0
Separate the equation into 2 possible cases
x=01−4x2+8x=0
Solve the equation
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Evaluate
1−4x2+8x=0
Rewrite in standard form
−4x2+8x+1=0
Multiply both sides
4x2−8x−1=0
Substitute a=4,b=−8 and c=−1 into the quadratic formula x=2a−b±b2−4ac
x=2×48±(−8)2−4×4(−1)
Simplify the expression
x=88±(−8)2−4×4(−1)
Simplify the expression
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Evaluate
(−8)2−4×4(−1)
Multiply
(−8)2−(−16)
Rewrite the expression
82−(−16)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
82+16
Evaluate the power
64+16
Add the numbers
80
x=88±80
Simplify the radical expression
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Evaluate
80
Write the expression as a product where the root of one of the factors can be evaluated
16×5
Write the number in exponential form with the base of 4
42×5
The root of a product is equal to the product of the roots of each factor
42×5
Reduce the index of the radical and exponent with 2
45
x=88±45
Separate the equation into 2 possible cases
x=88+45x=88−45
Simplify the expression
x=22+5x=88−45
Simplify the expression
x=22+5x=22−5
x=0x=22+5x=22−5
Solution
x1=22−5,x2=0,x3=22+5
Alternative Form
x1≈−0.118034,x2=0,x3≈2.118034
Show Solution