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$Solve for x. Enter the solutions from least to greatest. {:[(x+3)^(2)-4=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} (x+3)^{2}-4=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

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Evaluate exponential functions

Full solution

Q. Solve for

x

. Enter the solutions from least to greatest.

\newline

\begin{array}{l} (x+3)^{2}-4=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Expand and simplify the equation: Expand the squared term and simplify the equation. $\newline$ We start by expanding $(x+3)^2$ and then subtracting $4$ from both sides to simplify the equation. $\newline$ $(x+3)^2 - 4 = 0$ $\newline$ $(x+3)(x+3) - 4 = 0$ $\newline$ $x^2 + 6x + 9 - 4 = 0$ $\newline$ $x^2 + 6x + 5 = 0$
Factor the quadratic equation: Factor the quadratic equation. $\newline$ We need to factor the quadratic equation $x^2 + 6x + 5 = 0$ . We look for two numbers that multiply to $5$ and add up to $6$ . $\newline$ $(x + 5)(x + 1) = 0$
Solve for x using zero product property: Solve for x using the zero product property. $\newline$ We set each factor equal to zero and solve for x. $\newline$ $x + 5 = 0$ or $x + 1 = 0$ $\newline$ $x = -5$ or $x = -1$
Identify lesser and greater values of x: Identify the lesser and greater values of x. $\newline$ Comparing the two solutions, $-5$ is less than $-1$ . $\newline$ So, the lesser $x$ is $-5$ and the greater $x$ is $-1$ .

More problems from Evaluate exponential functions

Question

x

\newline

5^x=1

\newline

\newline

Write your answer in simplest form.

Posted 5 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

Posted 4 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

Posted 5 months ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 8 months ago

Question

x

\newline

7 = 9^x

\newline

Round your answer to the nearest thousandth.

Posted 4 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 7 months ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 9 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 7 months ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 4 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6x

\newline

f(x) = 6^x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 4 months ago

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