I need some help factoring part of an equation.
How would I factor -5(t^{2 }- 7t + 49/4). I do believe I have to factor it as a fraction but I have no clue what the fraction should be 2ab should equal -7t and b^{2 }is supposed to equal 49/4.
My guess is.. -5(t - 7/2)^{2} Is that correct?? Since technically 7/2 is 3.5.. And 3.5 x 2 = 7.. And then 7/2^{2 } should equal 49/4.
I would suggest for easy calculation just take LCM inside the braces and get rid of the denominator.
-5( t^2 - 7t + 49/4 ) = -5 [ ( 4t^2 - 28t + 49 )/4 ] = -5/4 ( 4t^2 - 28t + 49 ) . Now proceed with the steps for splitting the middle term
product of coefficient of x^2 and constant term = 4 * 49 = 2 * 2 * 7 * 7 = 14 * 14 = - 14 * - 14 Now we observe that the sum of these factors is indeed -28
Let us split the middle term
-5/4 ( 4t^2 - 28t + 49 ) = -5/4 ( 4t^2 - 14t - 14 t + 49 ) = -5/4 [ 2t ( 2t - 7 ) - 7 ( 2t - 7 ) ] = - 5/4 ( 2t-7 ) ( 2t - 7 ) = -5/4 ( 2t-7)^2