How do you solve this using completing the square? −16t^{2}+32t=−5-16t^{2} +32t=-5−16t^{2}+32t=−5

Daniaal Sanchez 2021-02-12 Answered
How do you solve this using completing the square? 16t2+32t=516t2+32t=516t2+32t=5
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Expert Answer

krolaniaN
Answered 2021-02-13 Author has 86 answers

To solve an equation by completing the square, you need to rewrite the expression to have a leading coefficient of 1.
Since the leading coefficient of 16t2+32t=5 is -16, you need to divide both sides by −16 to get a leading coefficient of 1. This gives t22t=516.
To complete the square for an expression of the form x2+bx, you need to add (b2)2.
For t22t,b=2 so you need to add (22)2=(1)2=1.
Adding 1 on both sides of t22t=516 then gives t22t+1=(516)+1 which simplifies to t22t+1=2116.
Now that the left side is a perfect square, you need to factor. Since x2+bx+(b2)2 factors to (x+b2), then t22t+1 factors to (t1)2 since b2=22=11.
The factored equation is then (t1)2=2116.
Square rooting both sides gives (t1)2=±2116 which simplifies to t1=±(214)
Adding 1 on both sides then gives t=1±214

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