/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 130 Solve each equation by the metho... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 130

Solve each equation by the method of your choice. $$\sqrt{3} x^{2}+6 x+7 \sqrt{3}=0$$

Short Answer

Expert verified
The solutions to the equation are \(x = -1 + 2i\sqrt{3}\) and \(x = -1 - 2i\sqrt{3}\).

Step by step solution

01

Identify the coefficients

The coefficients in the given equation are \(a = \sqrt{3}\), \(b = 6\), and \(c = 7\sqrt{3}\)
02

Substitute the coefficients into the quadratic formula

Substitute \(a = \sqrt{3}\), \(b = 6\), and \(c = 7\sqrt{3}\) into the quadratic formula. This results in, \[x = \frac{-6 \pm \sqrt{(6)^{2} - 4(\sqrt{3})(7\sqrt{3})}}{2\sqrt{3}}\]
03

Calculate the discriminant

Calculate the discriminant \(b^{2} - 4ac = (6)^{2} - 4(\sqrt{3})(7\sqrt{3})\). This simplifies to 36- 84 = -48. Since the discriminant is less than zero, the equation has two complex solutions.
04

Calculate the roots

Substitute the discriminant into the formula we have, \[x = \frac{-6 \pm \sqrt{-48}}{2\sqrt{3}}\], which simplifies to \[x = -1 \pm 2i\sqrt{3}\]

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Most popular questions from this chapter

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A local bank charges \(\$ 8\) per month plus 5 e per check. The credit union charges \(\$ 2\) per month plus 8 d per check. How many checks should be written each month to make the credit union a better deal?

This will help you prepare for the material covered in the next section. Is \(-1\) a solution of \(3-2 x \leq 11 ?\)

Solve absolute value inequality. \(|x|<3\)

Solve absolute value inequality. \(|x-1| \geq 2\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(1-\frac{x}{2}>4\)
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