How do you solve using the completing the square method $3x^2 + 15x = 9$ ?

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Answer 1 · 2016-03-09T06:50:17

$x=(-5+sqrt37)/2$ and $x=(-5-sqrt37)/2$

From the given

$3x^2+15x=9$

divide both sides of the equation by 3 first, to make the coefficient of $x^2$ equal to 1

$(3x^2)/3+(15x)/3=9/3$

$x^2+5x=3$

Divide now the numerical coefficient of x by 2 then square the result. Let the result be added to both sides of the equation

$x^2+5x+25/4=3+25/4$

We now have the Perfect Square Trinomial
$(x+5/2)^2=37/4$
Extract square root of both sides

$sqrt((x+5/2)^2)=sqrt(37/4)$

$x+5/2=+-1/2sqrt(37)$

$x=-5/2+-1/2sqrt(37)$

we have 2 values

$x=-5/2+1/2sqrt(37)$ and $x=-5/2-1/2sqrt(37)$

God bless....I hope the explanation is useful.

How do you solve using the completing the square method 3x^2 + 15x = 93x^2 + 15x = 9?