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To solve a quadratic equation by completing the square, follow these steps:
Isolate 'x' Terms
Move all terms containing 'x' to one side of the equation and shift the constant to the right.
Prepare for Perfect Square
Set up the left side for creating a perfect square, ensuring you balance the equation properly.
Calculate Half and Square
Take half of the coefficient of the 'x' term, square it, and add this value to both sides of the equation.
Simplify
Rewrite the left side as a perfect square expression.
Take Square Roots
Take the square root of both sides, remembering to consider both the positive and negative roots.
Solve for 'x'
Final step is to isolate 'x' to find the solution(s).
Some quadratic equations cannot be factored easily or yield irrational solutions. In such cases, the most reliable method is using the quadratic formula:
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}
\]
This formula can be used for solving any quadratic equation.
The Quadratic Equation Solver PRO APK is an advanced application designed to solve quadratic equations through detailed step-by-step explanations. It is distinct from other applications due to its dual methods:
Completing the Square
Quadratic Formula
Graph Generation
Capable of generating graphs based on given equations.
Step-by-Step Solutions
Offers detailed procedural breakdowns for better understanding.
Image Saving
Ability to save solutions as images for later reference.
User-Friendly Interface
Designed with a clean, material design layout.
Decimal and Fraction Support
Accepts both decimal and fractional numbers for input and output.
Imaginary Numbers Handling
Efficiently deals with imaginary numbers in solutions.
Basic Calculator Functionality
Each variable input functions like a simple calculator supporting arithmetic operators (*, /, +, -).
Lightweight Application
Optimized for smooth performance.
Quadratic equations are structured as \( ax^2 + bx + c = 0 \), where 'a', 'b', and 'c' are real numbers and 'a' cannot be zero. Each quadratic equation typically has two solutions, with the possibility of one solution being a duplicate. You can solve these equations using either the Completing the Square method or the Quadratic Formula.