Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the equation
2x^(2)+16 x+56=x^(2) to the nearest tenth.
Answer:
x=

Solve the equation $2 x^{2}+16 x+56=x^{2}$ to the nearest tenth. $\newline$ Answer: $x=$

View step-by-step help

View step-by-step help

Solve exponential equations using logarithms

Full solution

Q. Solve the equation

2 x^{2}+16 x+56=x^{2}

to the nearest tenth.

\newline

Answer:

x=

Set Equation to Zero: First, we need to set the equation to zero by moving all terms to one side. $\newline$ Subtract $x^2$ from both sides of the equation. $\newline$ $2x^2 + 16x + 56 - x^2 = x^2 - x^2$ $\newline$ This simplifies to: $\newline$ $x^2 + 16x + 56 = 0$
Factor or Use Formula: Next, we need to factor the quadratic equation if possible, or use the quadratic formula to find the values of $x$ . The quadratic equation is $x^2 + 16x + 56 = 0$ . Let's try to factor it. We are looking for two numbers that multiply to $56$ and add up to $16$ . The numbers $8$ and $7$ fit this requirement. So we can write the equation as: $(x + 8)(x + 7) = 0$
Apply Zero Product Property: Now, we apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. $\newline$ So we set each factor equal to zero and solve for $x$ : $\newline$ $x + 8 = 0$ or $x + 7 = 0$
Solve for x: Solve the first equation for x: $\newline$ $x + 8 = 0$ $\newline$ $x = -8$
Solve for x: Solve the second equation for x: $\newline$ $x + 7 = 0$ $\newline$ $x = -7$
Final Solutions: We have found two solutions for $x$ . They are $x = -8$ and $x = -7$ . Since we are asked to round to the nearest tenth, the solutions remain the same as they are already integers.

More problems from Solve exponential equations using logarithms

Question

Solve. Write your answer as an integer or a fraction in simplest form.

\newline

5^x=1

\newline

x=

Posted 2 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.

\newline

\$

Posted 2 months ago

Question

Use the following function rule to find

f(1)

\newline

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

\newline

f(1) =

Posted 1 month 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 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = 9^x

\newline

x =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 1 month ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 2 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 1 month 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 2 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) = 6^x

\newline

f(x) = 6x

\newline

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

\newline

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

Posted 2 months ago