In today’s digital age, students often rely on technology and online tools to solve algebraic problems effortlessly. Algebra Calculator like Mathway, Microsoft and MathPapa have become popular choices for quickly factoring algebraic expressions.
And now more powerful tool ChatGPT. Just write a prompt “Act as a Algebra Calculator and solve my quadratic and cubic equation step by step using factorisation method”
While these tools can be helpful for checking your work or solving simple problems, they should not replace the value of actual learning in algebra. And most important logic that you are a student and actually you have to solve in exam.
This article will discuss why students should stop relying solely on algebra calculators for factoring and instead embrace the importance of learning the fundamental concepts through examples.
Use Free Online Algebra Calculator For Factoring Quadratic Equation
Quadratic Equation Factoring Calculator
Enter the coefficients of the quadratic equation ax^2+bx+c=0 where a≠0 (must):
The general form of a quadratic equation is:
ax2 + bx + c=0
| Quadratic Equation | Coefficient |
|---|---|
| x² –x – 9 = 0 | a=1 | b=-1 | c=-9 |
| 5x² – 2x – 6 = 0 | a=5 | b=-2 | c=-6 |
| 3x² + 4x + 8 = 0 | a=3 | b=4 | c=8 |
| -x² +6x + 12 = 0 | a=1 | b=0 | c=-9 |
| x² -9 = 0 | a=1 | b=0 | c=-9 |
How to Solve Quadratic Equations Without Algebra Calculator?
There are three best methods of solving quadratic equations. They are:
- Factoring
- Completing the square
- Using Quadratic Formula
Factoring Method
1.Quadratic Equation: x^2 – 5x + 6 = 0
- Write down the equation: x^2 – 5x + 6 = 0
- Factor the equation: (x – 2)(x – 3) = 0
- Set each factor equal to zero and solve for x:
- x – 2 = 0 => x = 2
- x – 3 = 0 => x = 3
- The solutions are x = 2 and x = 3.
2.Quadratic Equation: 2x^2 + 7x – 3 = 0
- Write down the equation: 2x^2 + 7x – 3 = 0
- This equation doesn’t factor easily, so use another method.
3.Quadratic Equation: x^2 – 4x + 4 = 0
- Write down the equation: x^2 – 4x + 4 = 0
- Factor the equation: (x – 2)(x – 2) = 0
- Set the factor equal to zero and solve for x:
- x – 2 = 0 => x = 2
- The solution is x = 2.
Completing The Square Method
1.Quadratic Equation: x^2 + 6x – 8 = 0
- Write down the equation: x^2 + 6x – 8 = 0
- Move the constant term to the other side: x^2 + 6x = 8
- Complete the square by adding and subtracting (6/2)^2 = 9 to the left side:
- x^2 + 6x + 9 – 9 = 8
- Factor the perfect square trinomial on the left side: (x + 3)^2 = 17
- Take the square root of both sides:
- x + 3 = ±√17
- fSolve for x:
- x = -3 ± √17
2.Quadratic Equation: 4x^2 – 12x + 9 = 0
- Write down the equation: 4x^2 – 12x + 9 = 0
- Divide the entire equation by 4 to simplify: x^2 – 3x + 2.25 = 0
- Complete the square:
- x^2 – 3x + (3/2)^2 = 2.25 + (3/2)^2
- Factor the perfect square trinomial on the left side: (x – 1.5)^2 = 6.25
- Take the square root of both sides:
- x – 1.5 = ±√6.25
- fSolve for x:
- x = 1.5 ± √6.25
Using Quadratic Formula
1.Quadratic Equation: 2x^2 – 5x + 3 = 0
- Write down the equation: 2x^2 – 5x + 3 = 0
- Use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a)
- where a = 2, b = -5, and c = 3
- Plug in the values and solve for x:
- x = (-(-5) ± √((-5)² – 4(2)(3))) / (2(2))
- x = (5 ± √(25 – 24)) / 4
- x = (5 ± √1) / 4
- Simplify:
- x = (5 ± 1) / 4
- The solutions are x = 3/2 and x = 1/2.
Quadratic Equation: 4x^2 + 8x + 4 = 0
- Write down the equation: 4x^2 + 8x + 4 = 0
- Use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a)
- where a = 4, b = 8, and c = 4
- Plug in the values and solve for x:
- x = (-8 ± √(8² – 4(4)(4))) / (2(4))
- x = (-8 ± √(64 – 64)) / 8
- x = (-8 ± √0) / 8
- Simplify:
- x = (-8 ± 0) / 8
- The only solution is x = -1.
You Should Avoid Using Algebra Calculator in 2023
In 2023, it’s a good idea for students to not rely too much on algebra calculators when learning math. Here are 10 simple reasons why:
- Understanding Math: Calculators might give answers, but they don’t help you really get math.
- Thinking Skills: Doing math by hand helps you think better and solve problems in everyday life.
- Being Confident: If you can solve math without a calculator, you’ll feel more confident in your abilities.
- Exams: In many tests, you can’t use calculators, so you need to know how to do it without one.
- Learning Steps: Doing math manually helps you understand how math works.
- Mistakes: Relying on calculators can lead to mistakes when typing numbers or reading results.
- Advanced Math: You need good math skills to tackle harder math beyond what calculators can do.
- Real-Life Skills: Math is useful for things like money, making decisions, and solving everyday problems.
- Everyday Life: Math is important in everyday life, not just in school.
- Help from Teachers: Teachers can see how well you understand math when you solve problems without calculators, and they can help you better.
So, while calculators can be handy, it’s better to learn math without relying on them too much. It’ll make you better at math and help you in many other parts of life.