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Calculator: (x+a)^2=b
The calculator for (x+a)^2=b is a simple online tool that helps you solve quadratic equations of the form (x+a)^2=b. In this article, we will explore how to use this calculator and learn about the mathematical concept behind it.
What is (x+a)^2=b?
(x+a)^2=b is a quadratic equation, where x is the variable, a is a constant, and b is another constant. Expanding the equation, we get:
x^2 + 2ax + a^2 = b
How to use the (x+a)^2=b calculator?
Using the calculator is straightforward. Here are the steps:
Step 1: Enter the values of a and b
Enter the values of a and b in the respective input fields.
Step 2: Click the "Calculate" button
Click the "Calculate" button to get the solution.
Step 3: Get the solution
The calculator will display the solutions for x.
Example:
Let's say you want to solve the equation (x+2)^2=9. Here's how you can use the calculator:
Step 1: Enter the values of a and b
Enter a=2 and b=9 in the input fields.
Step 2: Click the "Calculate" button
Click the "Calculate" button.
Step 3: Get the solution
The calculator will display the solutions for x, which are x=-5 and x=1.
Mathematical Concept:
The equation (x+a)^2=b is a quadratic equation, and its solutions can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a=1, b=2a, and c=a^2-b. Substituting these values into the quadratic formula, we get:
x = (± √(b - a^2)) - a
This formula will give us the solutions for x.
Conclusion:
The (x+a)^2=b calculator is a helpful tool for solving quadratic equations. By understanding the mathematical concept behind it, you can appreciate the beauty of mathematics and its applications. Whether you're a student or a professional, this calculator is a great resource to have at your fingertips.
