I think is <span> x = 7 or<span> x = -7
</span></span><span>Equation at the end of step 1 :</span><span> 3x2 - 147 = 0
</span><span>Step 2 :</span><span>Step 3 :</span>Pulling out like terms :
<span> 3.1 </span> Pull out like factors :
<span> 3x2 - 147</span> = <span> 3 • (x2 - 49)</span>
Trying to factor as a Difference of Squares :
<span> 3.2 </span> Factoring: <span> x2 - 49</span>
Theory : A difference of two perfect squares, <span> A2 - B2 </span>can be factored into <span> (A+B) • (A-B)
</span>Proof :<span> (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 <span>- AB + AB </span>- B2 =
<span> A2 - B2</span>
</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication.
Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.
Check : 49 is the square of 7
Check : <span> x2 </span>is the square of <span> x1 </span>
Factorization is : (x + 7) • (x - 7)
<span>Equation at the end of step 3 :</span><span> 3 • (x + 7) • (x - 7) = 0</span>
