document.write( "Question 229435: Find b2 - 4ac and the number of real solutions to each
\n" ); document.write( "equation. -3x2 + 7x = 0
\n" ); document.write( "The 2 next to the x is a to the power 2. I have no idea where to start for this problem how do I find b2 - ac, I do not understand anything it is saying in the readings either. Can someone please explain this to me in plain ole English???
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Algebra.Com's Answer #170117 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
You have obviously started learning about quadratic equaions and their solutions.
\n" ); document.write( "The standard form of the quadratic equation is:
\n" ); document.write( "\"ax%5E2%2Bbx%2Bc+=+0\" in which the a, b, and c are positive or negative numbers and the a is not equal to zero. If the a were equal to zero then you wouldn't have a quadratic equation.
\n" ); document.write( "You can always find the solutions to a quadratic equation by using the \"quadratic formula\" which looks like this:
\n" ); document.write( "\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"
\n" ); document.write( "The a, b, and c in this formula correspond the a, b, and c in the standard form given above.
\n" ); document.write( "The part of the quadratic formula that lies under the square root sign (\"b%5E2-4ac\") is called the \"discriminant\".
\n" ); document.write( "The value of the discriminant indicates the kind of roots (solutions) you can expect to find when you solve the quadratic equation.
\n" ); document.write( "If the value of the discriminant is positive, then the solution has two real roots.
\n" ); document.write( "If the value of the discriminant is negative, then the solution has two complex conjugate roots.
\n" ); document.write( "If the value of the discriminant is zero, then the soltion has one real root which is really two identical roots known as a double root.
\n" ); document.write( "In your quadratic equation:
\n" ); document.write( "\"-3x%5E2%2B7x+=+0\" a = -3, b = 7, and c = 0
\n" ); document.write( "The solutions for this equation are given by:
\n" ); document.write( "\"x+=+%28-7%2B-sqrt%287%5E2-4%28-3%29%280%29%29%29%2F2%28-3%29\" and here, the discriminant is:
\n" ); document.write( "\"7%5E2-4%28-3%29%280%29\" which evaluates to:
\n" ); document.write( "\"highlight%2849%29\" This is the value of \"b%5E2-4ac\"
\n" ); document.write( "Since this is positive, the solution to your equation has two real roots.
\n" ); document.write( "Let's solve your equation using the quadratic formula:\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\":
\n" ); document.write( "\"x+=+%28-7%2B-sqrt%287%5E2-4%28-13%29%280%29%29%29%2F2%28-3%29\"
\n" ); document.write( "\"x+=+%28-7%2B-sqrt%2849%29%29%2F%28-6%29\"
\n" ); document.write( "\"x+=+%28-7%2B7%29%2F%28-6%29\" or \"x+=+%28-7-7%29%2F%28-6%29%29\" and these can be simplified to:
\n" ); document.write( "\"highlight_green%28x+=+0%29\" or \"highlight_green%28x+=+2.33%29\" and these are the two real roots.\r
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