Solve each quadratic equation using the square root property. ...

Question

Solve each quadratic equation using the square root property. See Example 6. (3x - 1)² = 12

Accepted Answer

Hello, everyone. We are asked to use the square root property to solve the following quadratic equation for K. The equation we are given is in parentheses, eight K minus five squared equals 75. Our answer choices are A K equals the parentheses. Five minus five radical three closed parentheses divided by eight and open parentheses. Five plus five radical three closed parentheses divided by eight BK equals open parentheses. Five radical three minus five closed parentheses divided by eight open parentheses. Five radical three plus five closed parentheses divided by eight CK equals five fourths or zero DK equals negative five fourths or zero to begin with. I'm going to rewrite this equation. So eight K minus five in parentheses squared equals 75. The square root property says that we can take the square root of both sides to cancel a square. So we're gonna do that. And when we do, we are left with eight K minus five equals plus or minus the square root of 75. I know that I can reduce the square to 75. So I'm gonna do that off to the side and plug it back in. I recall that I can reduce radicals or square roots by breaking them down into factors. So I know that the square of 25 multiplied by the squared of three would equal the square of 75. And I know that the square to 25 is five. So five radical three is gonna be the same as the square to 75. So that's what we're gonna use going forward. So we have eight K minus five equals plus or minus five radical three. At this point, I'm gonna break this into two equations because eight K minus five could equal a positive five radical three or a negative. So we're gonna do both. So eight K minus five equals negative five radical three. And we also have the equation, eight K minus five equals positive five radical three. So first, I'm gonna solve eight K minus five equals negative five radical three. I'm gonna add five to both sides to cancel it out and try to isolate the K. So eight K equals five minus five radical three, then I will divide both sides by eight to get the K by itself. And so I get K equals five minus five radical three, all of which is divided by eight. So that's one of my values for eight K minus five equals a positive five radical three. I'm going to add five to both sides and we'll have eight K equals five plus five radical three. And recall you can't combine those because one has a radical and one doesn't. So it's kind of like like terms then to get the K by itself, I divide both sides by eight, they get K equals five plus five radical three, all of which is divided by eight. So this is our answer. These are our solutions for K and they match answer choice. A where K equals in parentheses, five minus five radical three closed parentheses divided by eight and the second one, open parentheses, five plus five radical three closed parentheses divided by eight have a nice day.

Solve each quadratic equation using the square root property. See Example 6. (3x - 1)² = 12

Key Concepts

Square Root Property

Isolating the Variable

Solving Linear Equations After Taking Square Roots

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