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Here is another proof of the quadratic formula. Begin with $a x^{2}+b x+c=0,$ and multiply each term of the equation by 4a. This gives $4 a^{2} x^{2}+4 a b x+4 a c=0 .$ Rewrite the equation as $4 a^{2} x^{2}+4 a b x=-4 a c$and add $b^{2}$ to each side giving $4 a^{2} x^{2}+4 a b x+b^{2}=b^{2}-4 a c$. Now factor the left-hand-side of this equation and complete the proof.

Algebra

Chapter 0

Reviewing the Basics

Section 4

The Quadratic Formula and Applications

Equations and Inequalities

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:00

Here are two steps from th…

02:42

The solutions of the quadr…

01:07

Prove that the numbers…

01:02

08:35

Use the Quadratic Formula …

03:34

Deriving the Quadratic For…

03:36

solve the given quadratic …

First We multiply both sides by four a. Which becomes for a squared X. Square plus for a big art past for a C. He kills your. Now then we subtract for a safe from both sides and then we have to be squared to both sides. Know that the left hand side is a perfect square now, which echoes to A X plus b squared. He calls the square miners for you see. And two years plus b equals plus all minors the square road out PC Square -4 is. And then they subtract B from both sides. At last It divided both sides by two. A. And this is just the result we want.

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