Need help Proving quadriatic equation

  • Thread starter princesscharming26
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In summary: To get rid of the square, take square roots: x+ b/2a= \pm\sqrt{(b2- 4ac)/(2a)}. Finally, solve for x: x= (-b/2a)\pm\sqrt{(b2- 4ac)/(2a)}.In summary, the conversation discusses the steps for completing the square in order to solve a quadratic equation. This includes dividing both sides by a, adding the square of half of the coefficient of x to both sides, and taking the square root to eliminate the square. The final solution for x is (-b/2a)±√((b2- 4ac)/(2a)).
  • #1
princesscharming26
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I need help proving the quadriatic equation... this is all i got up to:

ax(squared)+bx+(b/2)quantity squared= -c+(b/2)quantity squared

:frown:

sorry.. i kind of don't know how to use the other codes!
:confused:
 
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  • #2
Work your way backwards, then reverse the steps so you know the way forwards.

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Multiply both sides by 2a

[tex]2ax = -b \pm \sqrt{b^2 - 4ac}[/tex]

Add b to both sides

[tex]2ax + b = \pm \sqrt{b^2 - 4ac}[/tex]

Square both sides

[tex]4a^2x^2 + 4abx + b^2 = b^2 - 4ac[/tex]

Subtract [itex]b^2[/itex] from both sides

[tex]4a^2x^2 + 4abx = - 4ac[/tex]

Add 4ac to both sides

[tex]4a^2x^2 + 4abx + 4ac = 0[/tex]

Divide both sides by 4a

[tex]ax^2 + bx + c = 0 \ \dots \ (a \neq 0)[/tex]

So, to go forwards, do the opposite of those actions in reverse order:

Multiply both sides by 4a
Subtract 4ac from both sides
Add [itex]b^2[/itex] to both sides
Square root both sides
Subtract b from both sides
Divide both sides by 2a
 
  • #3
Or better is to complete the square on the original eqaution.
 
  • #4
matt grime said:
Or better is to complete the square on the original eqaution.

Exactly what I was going to say. Just complete the square with variables.
 
  • #5
Actually, the original post was trying to complete the square. Unfortunately, she was doing it wrong:

After writing ax2+ bx= -c, divide both sides by a: x2+ (b/a)x= -c/a.

NOW complete the square: the coefficient of x is (b/a) so we square half of that and add (b/2a)2 to both sides:
x2+ (b/a)x+ (b/2a)2= (b/2a)2- c/a

princesscharming26, do you understand WHY you add that square?

It's because x2+ (b/a)x+ (b/2a)2= (x+ b/2a)2.

Now you have (x+ b/2a)2= b2/4a- c/a= (b2- 4ac)/(2a).
 

FAQ: Need help Proving quadriatic equation

What is the quadratic equation?

The quadratic equation is a mathematical formula that is used to solve equations in the form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. It is commonly used to find the roots or solutions of a quadratic function.

How do you prove the quadratic equation?

There are a few different ways to prove the quadratic equation. One method is to use the quadratic formula, which is derived from completing the square on the general form of a quadratic equation. Another way is to use geometric proofs, which involve visual representations of the equation and its solutions.

Why is it important to prove the quadratic equation?

Proving the quadratic equation is important because it helps us to understand and verify the accuracy of the formula. It also allows us to use the equation in various applications, such as solving real-world problems or finding the maximum or minimum values of a quadratic function.

What are the common mistakes made when proving the quadratic equation?

Some common mistakes when proving the quadratic equation include using the wrong formula, incorrect application of algebraic rules, or making arithmetic errors. It is important to carefully check each step of the proof to ensure accuracy.

Can the quadratic equation be proven using different methods?

Yes, there are multiple methods for proving the quadratic equation, such as using the quadratic formula, completing the square, or using geometric proofs. Each method may provide a different perspective on the equation, but they all ultimately lead to the same solution.

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