Casey W. answered • 06/16/15

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Mathematics (and Science) Instruction by a Mathematician!

In general for a monic quadratic equation of the form:

x^2+bx=c, we can follow Mark's technique of writing

adding (b/2)^2 to both sides will make the left hand side a perfect square, (x+b/2)^2

x^2 + bx + (b/2)^2 = c + (b/2)^2

(x+b/2)^2 = c +(b/2)^2

And so we can then apply a square root (don't forget to introduce the +/-, obtained by expanding an absolute value), and subtracting b/2 from both sides:

(x+b/2) = +/- \sqrt{c+(b/2)^2}

x = -b/2 +/- \sqrt{c+(b/2)^2} (1)

x^2+bx=c, we can follow Mark's technique of writing

adding (b/2)^2 to both sides will make the left hand side a perfect square, (x+b/2)^2

x^2 + bx + (b/2)^2 = c + (b/2)^2

(x+b/2)^2 = c +(b/2)^2

And so we can then apply a square root (don't forget to introduce the +/-, obtained by expanding an absolute value), and subtracting b/2 from both sides:

(x+b/2) = +/- \sqrt{c+(b/2)^2}

x = -b/2 +/- \sqrt{c+(b/2)^2} (1)

Separate the constant terms and variable terms on either side of the equation, and multiply or divide by the leading coefficient to make the x^2 term have a coefficient of 1 in front (a monic equation)

2n^2+10n=-6 means n^2+5n = -3...and not that we can use b=5 and c=-3 in the formula (1) above.

z^2-14z = -34, means we can use b=-14 and c=-34 for the second problem!

Hope that helps!