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Chapter 0: Problem 61

Solve each quadratic equation by the square root property. $$3 x^{2}=27$$

Short Answer

Expert verified
The solutions to the equation \(3x^{2}=27\) are \(x=3\) and \(x=-3\).

Step by step solution

01

Simplify the Equation

First, divide both sides of the equation by 3 to simplify it: \(x^{2}=\frac{27}{3}\)
02

Solve for \(x^{2}\)

Now, solve the right side of the equation: \(x^{2}=9\)
03

Applying Square Root Property

Taking the square root on both sides of the above equation gives the possible solutions for x: \(x=\pm\sqrt{9}\)
04

Solve for x

Solving the above gives two possible values for x: \(x=\pm 3\)

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Most popular questions from this chapter

Will help you prepare for the material covered in the first section of the next chapter. If \(y=|x+1|,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -4 and ending with 2

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

Explain why \(|x|<-4\) has no solution.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2 x-1}{x-7}+\frac{3 x-1}{x-7}-\frac{5 x-2}{x-7}=0$$

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$
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