Questions: a^2+4a-32=0

a^2+4a-32=0
Transcript text: $a^{2}+4 a-32-0$
failed

Solution

failed
failed

Solution Steps

To solve the equation \(a^2 + 4a - 32 = 0\), we can use the quadratic formula, which is given by \(a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Here, the coefficients are \(a = 1\), \(b = 4\), and \(c = -32\). We will substitute these values into the quadratic formula to find the solutions for \(a\).

Step 1: Identify the Equation

We start with the quadratic equation given by

\[ a^2 + 4a - 32 = 0. \]

Step 2: Calculate the Discriminant

The discriminant \(D\) is calculated using the formula

\[ D = b^2 - 4ac, \]

where \(a = 1\), \(b = 4\), and \(c = -32\). Substituting these values, we find:

\[ D = 4^2 - 4 \cdot 1 \cdot (-32) = 16 + 128 = 144. \]

Step 3: Apply the Quadratic Formula

Using the quadratic formula

\[ a = \frac{-b \pm \sqrt{D}}{2a}, \]

we substitute \(b = 4\) and \(D = 144\):

\[ a = \frac{-4 \pm \sqrt{144}}{2 \cdot 1} = \frac{-4 \pm 12}{2}. \]

This gives us two solutions:

\[ a_1 = \frac{-4 + 12}{2} = \frac{8}{2} = 4.0, \]

\[ a_2 = \frac{-4 - 12}{2} = \frac{-16}{2} = -8.0. \]

Final Answer

The solutions to the equation \(a^2 + 4a - 32 = 0\) are

\[ \boxed{a = 4.0} \quad \text{and} \quad \boxed{a = -8.0}. \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Subtract the rational expressions. Reduce the final answer. 47/(2h-8) - 4/(h-4)
failedAnswered
Math 172: Integration July 30, 2020 1 "Area under the curve" Integration is often introduced as a way to solve the problem of calculating areas of objects with curved boundaries. That problem is then set up as a problem involving the graph of a function. So integration becomes an operation on functions. It turns out to have many more uses than expressing "area under the curve". Here is a sketch of how integration is typically defined along these lines. Suppose f is a real-valued function with domain containing a closed interval [a, b]. We will determine a way to find the area between the graph of f and the x-axis, from x=a to x=b : We'll start by approximating this area as a sum of areas of rectangles (somewhat like the picture suggests). Let's start with an example. Say f(x)=x^2. Say we want to find the area of the striped region (from x=1 to x=3, above the x-axis, and below the graph):
failedAnswered
A hardware company has sales agents in 4 states. The number of agents in each state is shown in the bar graph below. Using this bar graph, answer the questions.
failedAnswered
The equation of a circle is given in standard form. Complete parts a through c to follow the step by step process to sketch the graph of the circle. [ x^2+(y-4)^2=16 ] a) Determine the center and radius of the circle. The center of the circle is (Type an ordered pair.)
failedAnswered
Find the derivative of the function f(x) = 4 / (x - 1) using the limit definition of the derivative.