Question
Simplify the expression
80x5−13x−10x3
Evaluate
8x3×10x2−13x−220x3
Divide the terms
More Steps
Evaluate
220
Reduce the numbers
110
Calculate
10
8x3×10x2−13x−10x3
Solution
More Steps
Multiply the terms
8x3×10x2
Multiply the terms
80x3×x2
Multiply the terms with the same base by adding their exponents
80x3+2
Add the numbers
80x5
80x5−13x−10x3
Show Solution
Factor the expression
x(80x4−13−10x2)
Evaluate
8x3×10x2−13x−220x3
Multiply
More Steps
Multiply the terms
8x3×10x2
Multiply the terms
80x3×x2
Multiply the terms with the same base by adding their exponents
80x3+2
Add the numbers
80x5
80x5−13x−220x3
Divide the terms
More Steps
Evaluate
220
Reduce the numbers
110
Calculate
10
80x5−13x−10x3
Rewrite the expression
x×80x4−x×13−x×10x2
Solution
x(80x4−13−10x2)
Show Solution
Find the roots
x1=−2025+51065,x2=0,x3=2025+51065
Alternative Form
x1≈−0.685878,x2=0,x3≈0.685878
Evaluate
8x3×10x2−13x−220x3
To find the roots of the expression,set the expression equal to 0
8x3×10x2−13x−220x3=0
Multiply
More Steps
Multiply the terms
8x3×10x2
Multiply the terms
80x3×x2
Multiply the terms with the same base by adding their exponents
80x3+2
Add the numbers
80x5
80x5−13x−220x3=0
Divide the terms
More Steps
Evaluate
220
Reduce the numbers
110
Calculate
10
80x5−13x−10x3=0
Factor the expression
x(80x4−13−10x2)=0
Separate the equation into 2 possible cases
x=080x4−13−10x2=0
Solve the equation
More Steps
Evaluate
80x4−13−10x2=0
Solve the equation using substitution t=x2
80t2−13−10t=0
Rewrite in standard form
80t2−10t−13=0
Substitute a=80,b=−10 and c=−13 into the quadratic formula t=2a−b±b2−4ac
t=2×8010±(−10)2−4×80(−13)
Simplify the expression
t=16010±(−10)2−4×80(−13)
Simplify the expression
More Steps
Evaluate
(−10)2−4×80(−13)
Multiply
(−10)2−(−4160)
Rewrite the expression
102−(−4160)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
102+4160
Evaluate the power
100+4160
Add the numbers
4260
t=16010±4260
Simplify the radical expression
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Evaluate
4260
Write the expression as a product where the root of one of the factors can be evaluated
4×1065
Write the number in exponential form with the base of 2
22×1065
The root of a product is equal to the product of the roots of each factor
22×1065
Reduce the index of the radical and exponent with 2
21065
t=16010±21065
Separate the equation into 2 possible cases
t=16010+21065t=16010−21065
Simplify the expression
t=805+1065t=16010−21065
Simplify the expression
t=805+1065t=805−1065
Substitute back
x2=805+1065x2=805−1065
Solve the equation for x
More Steps
Substitute back
x2=805+1065
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±805+1065
Simplify the expression
x=±2025+51065
Separate the equation into 2 possible cases
x=2025+51065x=−2025+51065
x=2025+51065x=−2025+51065x2=805−1065
Solve the equation for x
More Steps
Substitute back
x2=805−1065
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±805−1065
Simplify the expression
x=±2051065−25i
Separate the equation into 2 possible cases
x=2051065−25ix=−2051065−25i
x=2025+51065x=−2025+51065x=2051065−25ix=−2051065−25i
x=0x=2025+51065x=−2025+51065
Solution
x1=−2025+51065,x2=0,x3=2025+51065
Alternative Form
x1≈−0.685878,x2=0,x3≈0.685878
Show Solution