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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

Happy Easter everyone!

I've just been revising some of my earlier a-level work and I'm a little confused with this:

"Let f(x) = x^2 + 6x + 7.

(a) Put f(x) into completed square form.

(b) Solve the equation f(x) = 4."

I do know how to do all of this but I can't for the life of me see where they are getting f(x) = 4 from?!

Aloha Nui means Goodbye.

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

Are they just saying that for the sake of the example that (x + 3)^2 - 2 = 4? That's mighty confusing since the next 50 pages that often use factorising and completing the square assume that f(x) = 0.

Aloha Nui means Goodbye.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

This is a traditional way to solve a quadratic equation.

Typically, you shift the original function into a form

f(x) = (x+a)²+b

It does no matter that the function equal to any given value, because the equation formed can be easily solved.

f(x)=c

(x+a)²=c-b

hence

Actually, given a equation of standard form, the explicit solution fomula is derived by this procedure

ax²+bx+c=0

a(x+b/2a)²=b²/4-c

......

**X'(y-Xβ)=0**

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**dimples****Member**- Registered: 2006-04-21
- Posts: 1

how can i write a two paragraph essay on "Solving Quadratic Equations by the Quadratic Formula"

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,591

Start here: Quadratic Equation Solver

Also here: Wikipedia

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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