Question
Factor the expression
3(x−7)(x+7)
Evaluate
3x2−147
Factor out 3 from the expression
3(x2−49)
Solution
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Evaluate
x2−49
Rewrite the expression in exponential form
x2−72
Use a2−b2=(a−b)(a+b) to factor the expression
(x−7)(x+7)
3(x−7)(x+7)
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Find the roots
x1=−7,x2=7
Evaluate
3x2−147
To find the roots of the expression,set the expression equal to 0
3x2−147=0
Move the constant to the right-hand side and change its sign
3x2=0+147
Removing 0 doesn't change the value,so remove it from the expression
3x2=147
Divide both sides
33x2=3147
Divide the numbers
x2=3147
Divide the numbers
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Evaluate
3147
Reduce the numbers
149
Calculate
49
x2=49
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±49
Simplify the expression
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Evaluate
49
Write the number in exponential form with the base of 7
72
Reduce the index of the radical and exponent with 2
7
x=±7
Separate the equation into 2 possible cases
x=7x=−7
Solution
x1=−7,x2=7
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