CONCEPT PREVIEW Use choices A–D to answer each question.

Question

A. 3x² - 17x - 6 = 0

B.(2x + 5)² = 7

C. x² + x = 12

D. (3x - 1) (x - 7) = 0

Which quadratic equation is set up for direct use of the square root property? Solve it.

Accepted Answer

Welcome back, everyone. We want to identify the quadratic equation that can be solved directly using the square root property and find its solution from the following list of equations A is X squared plus 10, X plus 25 equals zero B three, X minus seven, R squared equals 49 C four, X squared minus 12 X plus nine equals zero. And DX multiplied by X minus five plus six equals zero. No, the square root property. OK can be used on an equation that has a squared term. OK? And a constant term, but no linear term. In other words, it tells us that if we have an expression in the form U squared equals K, then U is going to be equal to plus or minus the square root of K. In other words, we find the square root of both sides for an equation that looks like this. So the question we have to ask ourselves when we look at these equations here, which one of them is written in a way that we can solve directly using the square root property. Well, even though A is a perfect square, it's not written in a form that it can be solved directly. We will have to do some adjustments there. When we look at B, it's written directly in that form because we have an expression that's being squared and equal to a constant. But then when we look at C and D, both of them don't fit the criteria. Therefore, B is the quadratic equation that can be solved directly using the square root property. And we are sure of that because if we write our equation three X minus seven squared equals 49. OK? And find the square root of both sides, then we get three X minus seven to be equal to plus or minus the square root of 49 which is equal to plus R minus seven. In that case, three X is going to be equal to seven plus or minus seven. OK? And no, if we split that up here because we know what plus or minus means that means either three X is going to be equal to seven plus seven, R, three X equals seven minus seven, seven plus seven equals 14. And if three X is 14, that must mean X is equal to 14 divided by three. While if three X equals seven minus 77 minus seven equals zero. And if three X equals zero, then X equals zero. So we were able to find both of those solutions. So we're pretty sure that B is the correct answer. Thanks a lot. For watching everyone. I hope this video helped.

CONCEPT PREVIEW Use choices A–D to answer each question.

A. 3x² - 17x - 6 = 0
B.(2x + 5)² = 7
C. x² + x = 12
D. (3x - 1) (x - 7) = 0

Which quadratic equation is set up for direct use of the square root property? Solve it.

Key Concepts

Quadratic Equations

Square Root Property

Factoring Quadratics

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