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3 years ago

Rewrite the equation by completing the square 2x^2-20x=x^2-19

Mathematics

2 answers:

Colt1911 [192]3 years ago

8 0

Answer:

Equation: (x - 10)² = 81

Soulotion: x = 10 + 9

Step-by-step explanation:

I tried it on khan academy

sergeinik [125]3 years ago

7 0

Answer:

x = -1, 19

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Standard Form: ax² + bx + c = 0
Factoring
Multiple Roots
Completing the Square: -b/(2a)

Step-by-step explanation:

Step 1: Define

2x² - 20x = x² - 19

Step 2: Solve for x

[Subtraction Property of Equality] Subtract x² on both sides: x² - 20x = -19
Complete the Square [Addition Property of Equality]: x² - 20x + 100 = -19 + 100
[Complete the Square] Simplify: (x - 10)² = 81
[Equality Property] Square root both sides: x - 10 = ±9
[Addition Property of Equality] Add 10 on both sides: x = 10 ± 9
Evaluate: x = -1, 19

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According to USA Today, customers are not settling for automobiles straight off the production lines. As an example, those who

MrMuchimi

Answer: $(24980.25,\ 25419.75)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : $n= 179$ , which is a large sample , so we apply z-test .

Sample mean : $\overline{x}=20200+5000=25200$

Standard deviation : $\sigma= 1500$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

Now, a confidence interval at the 95% level of confidence will be :-

$25200\pm(1.96)\dfrac{1500}{\sqrt{179}}\\\\\approx25200\pm219.75\\\\=(25200-219.75,\ 25200+219.75)\\\\=(24980.25,\ 25419.75)$

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4 years ago