How do you solve this using completing the square? −16t2+32t=−5−16t2+32t=−5−16t2+32t=−5

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krolaniaN · Accepted Answer

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 t2−2t=516. To complete the square for an expression of the form x2+bx, you need to add (b2)2. For t2−2t,b=−2 so you need to add (−22)2=(−1)2=1. Adding 1 on both sides of t2−2t=516 then gives t2−2t+1=(516)+1 which simplifies to t2−2t+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 t2−2t+1 factors to (t−1)2 since b2=−22=−11. The factored equation is then (t−1)2=2116. Square rooting both sides gives (t−1)2=±2116 which simplifies to t−1=±(214)​ Adding 1 on both sides then gives t=1±214

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

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