document.write( "Question 346644: How do I solve this quadratic equation?\r
\n" ); document.write( "\n" ); document.write( " x^2 +4x - 6 \n" ); document.write( "
Algebra.Com's Answer #247855 by CharlesG2(834)\"\" \"About 
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How do I solve this quadratic equation?\r
\n" ); document.write( "\n" ); document.write( " x^2 +4x - 6\r
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\n" ); document.write( "\n" ); document.write( "It is not an equation yet, it is a trinomial (a polynomial with 3 terms).
\n" ); document.write( "To solve it for x set it to 0 (zero).\r
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\n" ); document.write( "\n" ); document.write( "x^2 + 4x - 6 = 0
\n" ); document.write( "2 ways to solve this, either by factoring or by quadratic formula.\r
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\n" ); document.write( "\n" ); document.write( "factoring and then testing with FOIL (First Outer Inner Last):
\n" ); document.write( "-6 = -1 * 6 = 1 * -6 = -2 * 3 = 2 * - 3 (4 possibilities of factors)
\n" ); document.write( "(x - 1)(x + 6) --> outer and inner add to 5, so not work
\n" ); document.write( "(x + 1)(x - 6) --> outer and inner add to -5, so not work
\n" ); document.write( "(x - 2)(x + 3) --> outer and inner add to 1, so not work
\n" ); document.write( "(x + 2)(x - 3) --> outer and inner add to -1, so not work\r
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\n" ); document.write( "\n" ); document.write( "we are going to have to use the quadratic formula:
\n" ); document.write( "x^2 + 4x - 6 = 0 is of the form ax^2 + bx + c = 0,
\n" ); document.write( "where a = 1, b = 4, and c = -6
\n" ); document.write( "quadratic formula is:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "plug in values and solve:\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+4%5E2+-+4%2A1%2A-6+%29%29%2F%282%2A1%29+\"
\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+16+-+4%2A-6+%29%29%2F2+\"
\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+16+-+%28-24%29+%29%29%2F2+\"
\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+16+%2B+24+%29%29%2F2+\"
\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+40+%29%29%2F2+\"
\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+4%2A10+%29%29%2F2+\"
\n" ); document.write( "\"x+=+%28-4+%2B-+2%2Asqrt%28+10+%29%29%2F2+\"
\n" ); document.write( "\"x+=+-2+%2B-+sqrt%28+10+%29+\"
\n" ); document.write( "\"x1+=+-2+%2B+sqrt%28+10+%29+\"
\n" ); document.write( "\"x2+=+-2+-+sqrt%28+10+%29+\"\r
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\n" ); document.write( "\n" ); document.write( "x = -2 + sqrt(10) = 1.1623 rounded to 4 places
\n" ); document.write( "or x = -2 - sqrt(10) = -5.1623 rounded to 4 places\r
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\n" ); document.write( "\n" ); document.write( "check:
\n" ); document.write( "x^2 + 4x - 6 = 0
\n" ); document.write( "(-2 + sqrt(10))^2 + 4(-2 + sqrt(10)) - 6 = 0
\n" ); document.write( "4 + 2 * -2 * sqrt(10) + 10 - 8 + 4sqrt(10) - 6 = 0
\n" ); document.write( "4 - 4sqrt(10) + 2 + 4srt(10) - 6 = 0
\n" ); document.write( "6 - 6 = 0
\n" ); document.write( "0 = 0 , yes
\n" ); document.write( "(-2 - sqrt(10))^2 + 4(-2 - sqrt(10)) - 6 = 0
\n" ); document.write( "4 + 2 * -2 * -sqrt(10) + 10 - 8 - 4sqrt(10) - 6 = 0
\n" ); document.write( "4 + 4sqrt(10) + 2 - 4sqrt(10) - 6 = 0
\n" ); document.write( "6 - 6 = 0
\n" ); document.write( "0 = 0, yes\r
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