How do you solve 3p2+2=6p?

1 Answer
BDT Stu.
Dec 4, 2017

13(3±√3) . Get this answer by completing the square and making p the subject of the equation.

Explanation:

Rearrange the formula by bringing all values to one side of the equation.

3p2−6p+2=0

Leave the 2 in the formula but still ignore it and do simple factorisation on the rest.

3[p2−2p]+2=0

Now complete the square in the brackets like you would do when you are working with quadratic formulas with the coefficient of 1. In this equation the coefficient is 3 so it has to be factorised away.

3[(p−1)2−1]+2=0

Expand the square brackets only because we want the equation to remain completed.

3(p−1)2−3+2=0

Simplify by adding like term.

3(p−1)2−1=0

Rearrange the formula to make p the subject.

3(p−1)2=1
(p−1)2=13
p−1=±√13
p=1±√13

Tip! In the equation ax2+bx+c
the formula for completing the square is

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Rationalize the equation.

p=1±√1√3
p=1⋅√3√3±√1√3
p=√3√3±√1√3
p=√3±√1√3
p=√3±√1√3⋅√3√3
p=√3(√3±√1)√3⋅√3
p=√3⋅√3±(√3⋅√1)√3⋅√3
p=3±√33
p=13(3±√3)

Learn about rationalising at the following link
https://www.mathsisfun.com/algebra/rationalize-denominator.html

IF an exam question asks for two answers, write one answer with + sign instead of ± and the other with − sign.

In calculator exam questions, write the two answers in number form, but not surd.

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