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antiseptic1488 [7]
3 years ago
6

Solve 5x^2-2=-12 by taking the square root

Mathematics
1 answer:
k0ka [10]3 years ago
7 0

Answer:

x = ±i√2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality<u> </u>

<u>Algebra II</u>

Imaginary root <em>i</em>

  • <em>i</em> = √-1

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

5x² - 2 = -12

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Addition Property of Equality] Add 2 on both sides:                                    5x² = -10
  2. [Division Property of Equality] Divide 5 on both sides:                                 x² = -2
  3. [Equality Property] Square root both sides:                                                    x = ±√-2
  4. Rewrite:                                                                                                             x = ±√-1 · √2
  5. Simplify:                                                                                                             x = ±i√2
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we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"

Because one of these solutions does not have a meaning in the given contest.

<h3></h3><h3>Why is the statement incorrect?</h3>

So we have a square with an area of 16 square units, then the side length of that square will be given by:

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Now, there are two solutions for the above equation, these are:

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When we talk about dimensions of figures, negative numbers are not really well defined. We can't say that a square has a side length of "negative 4 units"

That does not make sense, remember that math is just a language, and it should be used to communicate things to others.

So the logical solutions (4 and -4) is not the only thing we need to look at when we state the solutions of a problem, but also the problem itself.

That is why we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"

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If you want to learn more about square roots:

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