document.write( "Question 35903: solve for x (3x-2)(x+5)=4x+2 \n" ); document.write( "
Algebra.Com's Answer #22067 by atif.muhammad(135)\"\" \"About 
You can put this solution on YOUR website!
x (3x-2)(x+5)=4x+2\r\n" );
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document.write( "Let's open up one of the brackets first\r\n" );
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document.write( "x(3x^2 + 15x - 2x - 10) = 4x + 2\r\n" );
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document.write( "Let's open up the last bracket\r\n" );
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document.write( "3x^3 + 15x^2 - 2x^2 - 10x = 4x + 2\r\n" );
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document.write( "Now let's move all the variables to the left hand side\r\n" );
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document.write( "3x^3 + 13x^2 -14x - 2 = 0 \r\n" );
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document.write( "Now we have a cubic equation.\r\n" );
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document.write( "To solve this, we use the factor theorem.\r\n" );
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document.write( "f(x) = 3x^3 + 13x^2 -14x - 2\r\n" );
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document.write( "When f(a) = 0, then (x-a) is a factor of f(x)\r\n" );
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document.write( "f(0) = -2\r\n" );
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document.write( "f(-1) = -3 + 13 + 14 -2 = 22\r\n" );
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document.write( "f(1) = 3 + 13 -14 -2 = 0\r\n" );
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document.write( "f(1) = 0, therefore (x-1) is a factor of f(x)\r\n" );
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document.write( "We now need to divide f(x) by (x-1) and find a quadratic equation.\r\n" );
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document.write( "I have 'magically' divided it. (using the long division method)\r\n" );
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document.write( "f(x) = (3x^2 + 16x + 2)(x-1)\r\n" );
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document.write( "We now have a quadratic and a linear.\r\n" );
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document.write( "(3x^2 + 16x + 2)(x-1)  = 0\r\n" );
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document.write( "Solve linear:\r\n" );
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document.write( "x-1 = 0\r\n" );
document.write( "x = 1 --> First solution\r\n" );
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document.write( "Solve quadratic:\r\n" );
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document.write( "3x^2 + 16x + 2 = 0\r\n" );
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"3x%5E2%2B16x%2B2+=+0\") has the following solutons:\r\n" );
document.write( "  \r\n" );
document.write( "  \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"\r\n" );
document.write( "  \r\n" );
document.write( "  For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.\r\n" );
document.write( "  \r\n" );
document.write( "  First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%2816%29%5E2-4%2A3%2A2=232\".\r\n" );
document.write( "  \r\n" );
document.write( "  Discriminant d=232 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-16%2B-sqrt%28+232+%29%29%2F2%5Ca\".\r\n" );
document.write( "  \r\n" );
document.write( "    \"x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+232+%29%29%2F2%5C3+=+-0.128075631378697\"\r\n" );
document.write( "    \"x%5B2%5D+=+%28-%2816%29-sqrt%28+232+%29%29%2F2%5C3+=+-5.20525770195464\"\r\n" );
document.write( "    \r\n" );
document.write( "    Quadratic expression \"3x%5E2%2B16x%2B2\" can be factored:\r\n" );
document.write( "  \"3x%5E2%2B16x%2B2+=+3%28x--0.128075631378697%29%2A%28x--5.20525770195464%29\"\r\n" );
document.write( "  Again, the answer is: -0.128075631378697, -5.20525770195464.\n" );
document.write( "Here's your graph:\n" );
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document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B16%2Ax%2B2+%29\"
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document.write( "We now know our 3 solutions!\r\n" );
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document.write( "x= 1, -5.21, -0.128
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