Solve each equation for the specified variable. (Assume no denomi...

Question

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. h = -16t^2+v_0t+s_0, for t

Accepted Answer

Hey, everyone here we are asked to solve for L in the following equation, Z is equal to negative nine L squared plus X L plus Y. So now our first step here is to rearrange our equation so that it equals to zero. So that means we just need to move our positive Z to the right side of our equation. And then we want to rearrange our equation such that we have have negative nine L squared plus X L plus Y minus Z is equal to zero. So now we want to treat L as the variable here since we are solving for L and that means we need to treat the other variables X Y and Z as constants. So this way we can apply the quadratic formula. So first, we need to recall the quadratic formula which using the variable L, we will know that L is equal to negative B plus or minus the square root of B squared minus four A C all divided by two A. So now we just need to identify our values for A B and C. So we can apply our quadratic formula. So, so starting with our value for A, well A is just the coefficient of L squared. So A is just negative nine. And now our value for B well B is just the coefficient of L. So be in our case is just X. And now for our value for C, we'll see are just the constants we have in our equation and we know that we're treating X Y and Z as constance. So the remaining constants, we have our Y and negative Z and this leaves us with C being these remaining constants. So C is Y minus Z. And so now that we have A B and C clearly identified according to our equation, we can go ahead and just substituting these values into our quadratic formula to solve for L. So here we have L is equal to negative X plus or minus the square root of X squared minus four times negative nine times the quantity of Y minus Z. And this is all divided by two times negative nine. And now we just need to work to simplify this expression on the right side. In doing this, we first have negative X plus or minus the square root of X squared. And then we have negative four times negative nine giving us positive 36 times the quantity of Y minus Z. And this is all divided by two times negative nine which simplifies to negative eight. And now continuing to simplify, we see that we have a negative value in our numerator. And we also have a negative value in the denominator. So both of the negative terms cancel and we get a positive value. So we have X plus or minus the square root of X squared plus 36 times the quantity of Y minus Z all divided by posit 18. And now we just have to finish up simplifying here by factoring in the 36 that's underneath the root. So we see that L is equal to X plus or minus the square root of X squared plus Y minus 36 Z all divided by 18. And with this, we have finished up simplifying and we have solved our original equation just for L. And so we are left with answer choice D. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. h = -16t^2+v_0t+s_0, for t