Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B....

Question

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 
Which equation is set up for direct use of the square root property? Solve it

Accepted Answer

Hey, everyone here, we are asked to select one of the following equations which can be directly solved by using the square root property. And then we need to work out the values of X. So if we recall the square root property, we know that we use it when we solve quadratic equations, which we need to eliminate the square components so that we can isolate the variable being solved. So if we look at our given equation, we see that this property directly applies to equation to where we have the quantity of three X plus one squared is equal to four. And we know that the square root property applies to this equation because we have this square exponents here on the left side of our equation. And we need to get rid of this square so that we can isolate X. So now to do this, to apply the square root property, we just need to begin by taking the square root of both sides of the equation. So on the left hand side, we take the square root to get rid of the square exponents. And then on the right hand side, we take the square root of four. But we need to remember to input this plus or minus in front of the square root of four. So with this, now we can just simplify. So the left hand side simplifies to just three X plus one. And then on the right hand side, we have plus or minus two. So now we see because of this plus or minus two, we will have two separate solutions and two different equations to solve one, which we will have a positive two and the other, which we will have a negative two. So we can start with the P positive too. So we have three X plus one is equal to positive two. And now we just need to solve for X by isolating the variable. So we just need to first subtract one from both sides and we have three X is equal to one. And now we need to get rid of the coefficient of X. So we just need to divide both sides by three. And we see that one solution for X is just one third. And so now we can move on to our second equation where we will have negative two. So we have three, X plus one is equal to negative two. And now again, we just need to solve for X. So first, we subtract one from both sides and we have three, X is equal to negative three. And now getting rid of the coefficient we divide both sides by three. And we see that the solution for X is just negative one. So now we see that using equation to applying the square root property, we have come up with two solutions for X, we have come up with one third and negative one. So with this, we have, we are left with just 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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Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the square root property? Solve it