Solver Completing the Square for Quadratics

Source code of 'Completing the Square for Quadratics'

This Solver (Completing the Square for Quadratics) was created by by Shin123(626)

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==section input
Complete the square for the quadratic *[input a=1]x2+*[input b=-5]x+*[input c=6]=0. If you want all solutions, including imaginary solutions, toggle imaginary solutions on *[choice sol real-solutions imaginary-solutions] <----------

==section solution
perl
$X=x;

if ($b<0) {
 $bb=-$b;
 $sign="-";
 } else {
 $bb=$b;
 $sign="+";
 }
 if ($c<0) {
 $cc=-$c;
 $signa="-";
 } else {
 $cc=$c;
 $signa="+";
 }

if ($a == 1) {
# if ($b<0) {
 #$bb=-$b;
 # $sign="-";
# } else {
# $bb=$b;
 #$sign="+";
 # }
# if ($c<0) {
 # $cc=-$c;
 #$signa="-";
# } else {
 #$cc=$c;
 # $signa="+";
 # }
 print("To complete the square for the quadratic {{{x^2$sign$bb*x$signa$cc=0}}}, we must first find a square which when expanded, has x2 and $b$X in it.\n\n");
 $b1 = $b/2;
 if ($b1<0) {
 $signb1="-";
 $b1b1=-$b1;
 } else {
 $signb1="+";
 $b1b1=$b1;
 }
 $b4=$c-($b1 ** 2);
 if ($b4<0) {
 $b4b4=-$b4;
 $signb4="-";
 } else {
 $b4b4=$b4;
 $signb4="+";
 }
 print("{{{(x$signb1$b1b1)^2}}} is the square we are looking for. Expanding {{{(x$signb1$b1b1)^2}}} gets {{{x^2$sign$bb*x+" . ($b1 ** 2) . "}}}. So we have {{{x^2$sign$bb*x+$c=(x$signb1$b1b1)^2$signb4$b4b4}}}. So completing the square gives {{{x^2$sign$bb*x+$c=highlight((x$signb1$b1b1)^2$signb4$b4b4)}}}.\n ");
 #$b4 = $c-($b1 ** 2);
 if (-($b4) < 0) {
 print("Subtracting $b4 from both sides, we get {{{(x$signb1$b1b1)^2=-$b4}}}. Since the right side is negative, there are no real solutions.");
 if ($sol eq "imaginary-solutions") {
 print(" However, there are two imaginary solutions.");
 $q1=$b4;
 $q2=$q1 ** 0.5;
 $q3=-$b1;
 print("Taking the square root of both sides gives {{{system(x$signb1$b1b1= sqrt($q1)*i=$q2*i,x$signb1$b1b1 = -sqrt($q1)*i=-$q2*i)}}}. The two solutions are {{{system($q3+$q2*i,$q3-$q2*i)}}} ");
 }
 } elsif(-($b4)>0) {
 $b5 = -($b4);
 $b6 = $b5 ** 0.5;
 $ans1 = $b6-$b1;
 $ans2 = (-$b6)-$b1;
 print("Adding $b5 from both sides, we get {{{(x$signb1$b1b1)^2=$b5}}}. Taking the square root of both sides gives {{{system(x$signb1$b1b1=sqrt($b5)=$b6,x$signb1$b1b1=-sqrt($b5)=" . (-($b6)) . ")}}}. {{{system(x=$ans1,x=$ans2)}}} So the solutions are x=" . ($b6-$b1) . " and x=" . ((-$b6)-$b1) . ".");
 } else {
 print("So we have the equation {{{(x+$b1)^2=0}}}. There is only one unique solution. x=" . (-($b1)) . ".");
 }
} elsif($a!=0) {
 print("To complete the square for the quadratic {{{$a*x^2$sign$bb*x$signa$cc=0}}}, we must first find a square which when expanded, has $a$X2 and $b$X in it.\n\n");
 $b2 = $b/$a;
 $c2 = $c/$a;
 $b1 = $b2/2;
 if ($b2<0) {
 $b2b2=-$b2;
 $signb2="-";
 } else {
 $b2b2=$b2;
 $signb2="+";
 }
 if ($c2<0) {
 $c2c2=-$c2;
 $signc2="-";
 } else {
 $c2c2=$c2;
 $signc2="+";
 }
 if ($b1<0) {
 $b1b1=-$b1;
 $signb1="-";
 } else {
 $b1b1=$b1;
 $signb1="+";
 }
 $b4=$c2-($b1 ** 2);
 if ($b4<0) {
 $b4b4=-$b4;
 $signb4="-";
 } else {
 $b4b4=$b4;
 $signb4="+";
 }
 print("Factoring $a from the left side gives {{{$a(x^2$signb2$b2b2*x$signc2$c2c2)=0}}}. {{{(x$signb1$b1b1)^2}}} is the square we are looking for. So we get {{{$a((x$signb1$b1b1)^2$signb4$b4b4)=0}}}.\n");
 $b3 = $a*($c2-($b1 ** 2));
# $b4 = $c2-($b1 ** 2);
 if ($b3<0) {
 $b3b3=-$b3;
 $signb3="-";
 } else {
 $b3b3=$b3;
 $signb3="+";
 }
 print("Taking the $b4 out of the $a, we get {{{highlight($a(x$signb1$b1b1)^2$signb3$b3b3)}}}.");
 if (-($b3) < 0) {
 print(" Subtracting $b3 from both sides, we get {{{$a((x$signb1$b1b1)^2)=-$b3}}}. Since the right side is negative, there are no real solutions.");
 if ($sol eq "imaginary-solutions") {
 print(" However, there are two imaginary solutions. Dividing both sides by $a gives {{{(x$signb1$b1b1)^2=" . (-($b3)/$a) . "}}}.");
 $q1=$b3/$a;
 $q2=$q1 ** 0.5;
 $q3=-$b1;
 print("Taking the square root of both sides gives {{{system(x$signb1$b1b1=sqrt($q1)*i=$q2*i,x$signb1$b1b1=-sqrt($q1)*i=-$q2*i)}}}. The two solutions are {{{system($q3+$q2*i,$q3-$q2*i)}}} ");
 }
 } elsif(-($b3)>0) {
 $b5 = -($b3);
 $b7 = $b5/$a;
 $b6 = $b7 ** 0.5;
 $ans1 = $b6-$b1;
 $ans2 = (-$b6)-$b1;
 print(" Adding $b5 to both sides, we get {{{$a((x$signb1$b1b1)^2)=$b5}}}. Dividing both sides by $a gives {{{(x$signb1$b1b1)^2=$b7}}}. ");
 if($b7<0) {
 print("Since $b7 is negative, there are no real solutions.");
 if($sol eq "imaginary-solutions") {
 $O="i";
 print("However, there are two imaginary solutions. Taking the square root of both sides gives {{{system(x+$signb1$b1b1=" . ((-$b7)**0.5) . "*i,x+$signb1$b1b1=-" . ((-$b7)**0.5) . "*i)}}}. So the solutions are {{{-$b1+" . ((-$b7)**0.5) . "$O}}} and {{{-$b1-" . ((-$b7)**0.5) . "$O}}}.");
 }
 } else {
 print("Taking the square root of both sides gives {{{system(x$signb1$b1b1=sqrt($b7)=$b6,x$signb1$b1b1=-sqrt($b7)=" . (-($b6)) . ")}}}. {{{system(x=$ans1,x=$ans2)}}} So the solutions are x=" . ($b6-$b1) . " and x=" . ((-$b6)-$b1) . ".");
 }
 } else {
 print("So we have the equation {{{$a(x$signb1$b1b1)^2=0}}}. Dividing both sides by $a gives {{{(x$signb1$b1b1)^2=0}}}. There is only one unique solution. x=" . (-($b1)) . ".");
 }
}
elsif($b!=0) {
 print "Since the coefficient of the x^2 term is zero, this is not a quadratic.";
 if($b==69) {
 if($c==42) {
 print "nice";
 }
 }
}
==section output

==section check

==section practice 
perl

my $a1 = randint(-5,5);
  while($a1==0) {
    $a1=randint(-5,5);
  }
  my $a2 = randint(-5,5);
  while($a2==0) {
    $a2=randint(-5,5);
  }
  my $a3 = randint(1,3);
  $a = $a3;
  $b = -$a3*($a1+$a2);
  $c = $a1*$a2*$a3;