Question
Factor the expression
2(x−30)(x+30)
Evaluate
2x2−1800
Factor out 2 from the expression
2(x2−900)
Solution
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Evaluate
x2−900
Rewrite the expression in exponential form
x2−302
Use a2−b2=(a−b)(a+b) to factor the expression
(x−30)(x+30)
2(x−30)(x+30)
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Find the roots
x1=−30,x2=30
Evaluate
2x2−1800
To find the roots of the expression,set the expression equal to 0
2x2−1800=0
Move the constant to the right-hand side and change its sign
2x2=0+1800
Removing 0 doesn't change the value,so remove it from the expression
2x2=1800
Divide both sides
22x2=21800
Divide the numbers
x2=21800
Divide the numbers
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Evaluate
21800
Reduce the numbers
1900
Calculate
900
x2=900
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±900
Simplify the expression
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Evaluate
900
Write the number in exponential form with the base of 30
302
Reduce the index of the radical and exponent with 2
30
x=±30
Separate the equation into 2 possible cases
x=30x=−30
Solution
x1=−30,x2=30
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