document.write( "Question 134317: Solve the following equation by completing the square\r
\n" ); document.write( "\n" ); document.write( "x2-8x+15=0\r
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Algebra.Com's Answer #98233 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!

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Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

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\n" ); document.write( " \"y=1+x%5E2-8+x%2B15\" Start with the given equation
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\n" ); document.write( " \"y-15=1+x%5E2-8+x\" Subtract \"15\" from both sides
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\n" ); document.write( " \"y-15=1%28x%5E2-8x%29\" Factor out the leading coefficient \"1\"
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\n" ); document.write( " Take half of the x coefficient \"-8\" to get \"-4\" (ie \"%281%2F2%29%28-8%29=-4\").
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\n" ); document.write( " Now square \"-4\" to get \"16\" (ie \"%28-4%29%5E2=%28-4%29%28-4%29=16\")
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\n" ); document.write( " \"y-15=1%28x%5E2-8x%2B16-16%29\" Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of \"16\" does not change the equation
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\n" ); document.write( " \"y-15=1%28%28x-4%29%5E2-16%29\" Now factor \"x%5E2-8x%2B16\" to get \"%28x-4%29%5E2\"
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\n" ); document.write( " \"y-15=1%28x-4%29%5E2-1%2816%29\" Distribute
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\n" ); document.write( " \"y-15=1%28x-4%29%5E2-16\" Multiply
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\n" ); document.write( " \"y=1%28x-4%29%5E2-16%2B15\" Now add \"15\" to both sides to isolate y
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\n" ); document.write( " \"y=1%28x-4%29%5E2-1\" Combine like terms
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\n" ); document.write( " Now the quadratic is in vertex form \"y=a%28x-h%29%5E2%2Bk\" where \"a=1\", \"h=4\", and \"k=-1\". Remember (h,k) is the vertex and \"a\" is the stretch/compression factor.
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\n" ); document.write( " Check:
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\n" ); document.write( " Notice if we graph the original equation \"y=1x%5E2-8x%2B15\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2-8x%2B15%29\" Graph of \"y=1x%5E2-8x%2B15\". Notice how the vertex is (\"4\",\"-1\").
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\n" ); document.write( " Notice if we graph the final equation \"y=1%28x-4%29%5E2-1\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x-4%29%5E2-1%29\" Graph of \"y=1%28x-4%29%5E2-1\". Notice how the vertex is also (\"4\",\"-1\").
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\n" ); document.write( " So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.
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