document.write( "Question 367314: Good evening, I'm having trouble finding the x-intercept of the following equation:\r
\n" ); document.write( "\n" ); document.write( "\"2x%5E2%2B16x%2B9\"\r
\n" ); document.write( "\n" ); document.write( "I already managed to complete the square to get the vertex form:\r
\n" ); document.write( "\n" ); document.write( "\"2%28x%2B4%29%5E2+-+23\"\r
\n" ); document.write( "\n" ); document.write( "The y-intercept is 9, obtained by plugging 0 in for x and solving for y.\r
\n" ); document.write( "\n" ); document.write( "The vertex is (4, -23), but I don't understand how to find the x-intercept. I graphed the equation and the x-intercepts are somewhere around (-7.5, 0) and (-0.6, 0) but I have no idea how to calculate these. Please help! Your time is much, MUCH appreciated :)
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Algebra.Com's Answer #261820 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
There are two ways to do this. Both methods involve setting each expression equal to zero.\r
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\n" ); document.write( "\n" ); document.write( "\"2x%5E2%2B16x%2B9=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic \"2x%5E2%2B16x%2B9\" is in the form of \"Ax%5E2%2BBx%2BC\" where \"A=2\", \"B=16\", and \"C=9\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for \"x\":\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%2816%29+%2B-+sqrt%28+%2816%29%5E2-4%282%29%289%29+%29%29%2F%282%282%29%29\" Plug in \"A=2\", \"B=16\", and \"C=9\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-16+%2B-+sqrt%28+256-4%282%29%289%29+%29%29%2F%282%282%29%29\" Square \"16\" to get \"256\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-16+%2B-+sqrt%28+256-72+%29%29%2F%282%282%29%29\" Multiply \"4%282%29%289%29\" to get \"72\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-16+%2B-+sqrt%28+184+%29%29%2F%282%282%29%29\" Subtract \"72\" from \"256\" to get \"184\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-16+%2B-+sqrt%28+184+%29%29%2F%284%29\" Multiply \"2\" and \"2\" to get \"4\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-16+%2B-+2%2Asqrt%2846%29%29%2F%284%29\" Simplify the square root (note: If you need help with simplifying square roots, check out this solver) \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-16%2B2%2Asqrt%2846%29%29%2F%284%29\" or \"x+=+%28-16-2%2Asqrt%2846%29%29%2F%284%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-8%2Bsqrt%2846%29%29%2F%282%29\" or \"x+=+%28-8-sqrt%2846%29%29%2F%282%29\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"x+=+%28-8%2Bsqrt%2846%29%29%2F%282%29\" or \"x+=+%28-8-sqrt%2846%29%29%2F%282%29\" \r
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\n" ); document.write( "\n" ); document.write( "This means that the x-intercepts are and \r
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\n" ); document.write( "\n" ); document.write( "Method 2: \r
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\n" ); document.write( "\n" ); document.write( "\"2%28x%2B4%29%5E2-23=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x%2B4%29%5E2=0%2B23\"Add \"23\" to both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x%2B4%29%5E2=23\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B4%29%5E2=%2823%29%2F%282%29\" Divide both sides by \"2\".\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B4=%22%22%2B-sqrt%2823%2F2%29\" Take the square root of both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B4=sqrt%2823%2F2%29\" or \"x%2B4=-sqrt%2823%2F2%29\" Break up the \"plus/minus\" to form two equations.\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B4=sqrt%2846%29%2F2\" or \"x%2B4=-sqrt%2846%29%2F2\" Simplify the square root.\r
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\n" ); document.write( "\n" ); document.write( "\"x=-4%2Bsqrt%2846%29%2F2\" or \"x=-4-sqrt%2846%29%2F2\" Subtract \"4\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"x=%28-8%2Bsqrt%2846%29%29%2F%282%29\" or \"x=%28-8-sqrt%2846%29%29%2F%282%29\" Combine the fractions.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"x=%28-8%2Bsqrt%2846%29%29%2F%282%29\" or \"x=%28-8-sqrt%2846%29%29%2F%282%29\".\r
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\n" ); document.write( "\n" ); document.write( "So again, the x-intercepts are and \r
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\n" ); document.write( "\n" ); document.write( "Note: The approximate form of the x-intercepts is x-intercepts are and \r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my tutoring website\r
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\n" ); document.write( "\n" ); document.write( "Jim
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