Question
Simplify the expression
150x2−1
Evaluate
25x3×x6−1
Solution
More Steps

Multiply the terms
25x3×x6
Cancel out the common factor x
25x2×6
Multiply the terms
150x2
150x2−1
Show Solution

Find the excluded values
x=0
Evaluate
25x3×x6−1
Solution
x=0
Show Solution

Find the roots
x1=−306,x2=306
Alternative Form
x1≈−0.08165,x2≈0.08165
Evaluate
25x3×x6−1
To find the roots of the expression,set the expression equal to 0
25x3×x6−1=0
Find the domain
25x3×x6−1=0,x=0
Calculate
25x3×x6−1=0
Multiply the terms
More Steps

Multiply the terms
25x3×x6
Cancel out the common factor x
25x2×6
Multiply the terms
150x2
150x2−1=0
Move the constant to the right-hand side and change its sign
150x2=0+1
Removing 0 doesn't change the value,so remove it from the expression
150x2=1
Divide both sides
150150x2=1501
Divide the numbers
x2=1501
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±1501
Simplify the expression
More Steps

Evaluate
1501
To take a root of a fraction,take the root of the numerator and denominator separately
1501
Simplify the radical expression
1501
Simplify the radical expression
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Evaluate
150
Write the expression as a product where the root of one of the factors can be evaluated
25×6
Write the number in exponential form with the base of 5
52×6
The root of a product is equal to the product of the roots of each factor
52×6
Reduce the index of the radical and exponent with 2
56
561
Multiply by the Conjugate
56×66
Multiply the numbers
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Evaluate
56×6
When a square root of an expression is multiplied by itself,the result is that expression
5×6
Multiply the terms
30
306
x=±306
Separate the equation into 2 possible cases
x=306x=−306
Check if the solution is in the defined range
x=306x=−306,x=0
Find the intersection of the solution and the defined range
x=306x=−306
Solution
x1=−306,x2=306
Alternative Form
x1≈−0.08165,x2≈0.08165
Show Solution
