Solve Quadratic Equations Game (a > 1)
Solving a quadratic equation means finding the value(s) of the variable that make the equation true. A quadratic equation is an equation that can be written in the standard form: ax² + bx + c = 0, where a, b, and c are coefficients. Scroll down the page for a more detailed explanation.
 
Thus game will require you to solve a quadratic equation where the coefficient of x² is greater 1. The solutions may be fractions. If you get an answer wrong, the game will show you the correct solution.
 
Check out this other two games:
Solve Quadratic Equations (a = 1)
Solve Quadratic Equations (use the quadratic formula)
 

Quadratic Solver (Fractions)

Find the solutions for x. Enter answers as integers or fractions (e.g., 5/2 or -3).

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Check Next

Back to Menu

 

How to Play the Solve Quadratic Equations Game
Thus game will challenge you solve a quadratic equation where the coefficient of x² is greater than 1.
Here’s how to play:

1. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
2. Look at the Problem: You’ll be given a quadratic equation in the form x² + bx + c = 0.
   
3. Enter your answer: Enter the solutions for x.
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to Solve Quadratic Equations
To solve a quadratic equation of the form ax²+bx+c=0 where a>1, you can use one of several methods: the quadratic formula, factoring by grouping (or the “ac” method), or completing the square.
Method 1: The quadratic formula
This is the most universal method because it works for any quadratic equation, regardless of whether it can be factored.
( x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a} )
 
Method 2: Factoring by grouping (ac method)
Steps:

1. Multiply a and c. Find the product of the coefficient of x² (a) and the constant term (c).
   
2. Find two numbers that multiply to equal the product from Step 1 and add up to the coefficient of x (b).
   
3. Rewrite the equation by splitting the middle term ((bx)) using the two numbers found in Step 2.
   
4. Factor by grouping. Group the terms into pairs and find the greatest common factor (GCF) for each pair.
   
5. Set each factor to zero and solve for x.
    
   Method 3: Completing the square
   Steps:
   
6. Isolate the variable terms. Move the constant term c to the other side of the equation.
   
7. Divide by a. Divide the entire equation by the coefficient of x² (a).
   
8. Complete the square. Take half of the new coefficient of x, square it, and add it to both sides of the equation.
   
9. Factor the perfect square trinomial on one side and simplify the other.
   
10. Take the square root of both sides and solve for x.
     
    

The video gives a clear, step-by-step approach to solving quadratic equations.

• Show Video

 

Free Algebra Games
Distributive Property	Evaluate Algebraic Expressions	Evaluate Expressions (Exponents)
Simplify Algebraic Expressions	Solve Equations	Systems of Equations
Inequalities on the Number Line	Solve Inequalities	Multiply Binomials (y+b)(y+d)
Multiply Binomials (ay+b)(cy+d)	Factor Trinomials	Solve Quadratic Equations

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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