QUESTION(Quadratic Equations)
.Solve the equation x^2+12x+36=64
SOLUTION: =================
I shall do this with two methods as I am not sure which you are familiar with.
We have
x^2 + 12x + 36 = 64
x^2 + 12x + 36 - 64 = 0
x^2 + 12x - 28 = 0
Method 1 Factorise to get
(x - 2)(x + 14)=0
so,
x - 2 = 0 and x + 14 = 0
This gives x = 2, -14
Method 2 : Use the quadratic formula (see below in appendix)
This gives
x = [ - 12 \pm \sqrt{12^2 - 4(1)(-28)} ] / (2(1))
x = [ -12 \pm \sqrt{256} ] / 2
x = [ -12 \pm 16 ]/2
x = [-12 + 16]/2 ,\quad[-12-16]/2
x = 2, -14
CHECK:
when x = 2,
LHS = x^2 + 12x + 36
=2^2 +12(2) + 36
= 4 + 24 + 36
= 28 + 36
= 64 = RHS
when x = -14,
LHS = x^2 + 12x + 36
= (-14)^2 +12(-14) + 36
= 196 - 168 + 36
= 28 + 36
= 64 = RHS
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Appendix: The Quadratic Formula
The quadratic equation ax^2 + bx + c = 0 has solutions given by
x ={ -b \pm \sqrt{b^2 - 4ac} \over 2a}
Real solutions only exist provided b^2 - 4ac \ge 0.
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