How do you solve x^2 – 10x = 15 using completing the square?

2 Answers
Alan P.
Jun 22, 2015

x=5+-2sqrt(10)

Explanation:

x^2-10x = 15
color(white)("XXXX")If x^2-10x are the first two terms of a squared binominal
color(white)("XXXX")then the third term must be 25, since
color(white)("XXXX")color(white)("XXXX")(x-a)^2 = x^2-2ax+a^2
color(white)("XXXX")and, in this case a=5
x^2-10xcolor(blue)(+25) = 15+color(blue)(25)

(x-5)^2 = 40

color(white)("XXXX")Taking the square root of both sides gives
x-5 = +-2sqrt(10)

color(white)("XXXX")and finally
x = 5+-2sqrt(10)

Gió
Jun 22, 2015

I found:

x_1=5+sqrt(40)
x_2=5-sqrt(40)

Explanation:

You can add and subtract 25 to get:
x^2-10xcolor(red)(+25)color(red)(-25)=15
x^2-10x+25=15+25
(x-5)^2=40
x-5=+-sqrt(40)
So:
x_1=5+sqrt(40)
x_2=5-sqrt(40)

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