SOLUTION: Solve: 16x^2-72x=-85 Not sure if I'm suppose to factor or use the quadratic equation? Help would be appreciated! :)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve: 16x^2-72x=-85 Not sure if I'm suppose to factor or use the quadratic equation? Help would be appreciated! :)       Log On


   

Question 751745: Solve: 16x^2-72x=-85
Not sure if I'm suppose to factor or use the quadratic equation? Help would be appreciated! :)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+16x%5E2-72x=-85+
I don't know which method they want you to use, but
I can try completing the square
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First, divide both sides by +16+
+x%5E2+-+%289%2F2%29%2Ax+=+-85%2F16+
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Take 1/2 of the coefficient of +x+,
square it, and add it to both sides
+x%5E2+-+%289%2F2%29%2Ax+%2B+%289%2F4%29%5E2+=+-85%2F16+%2B+%289%2F4%29%5E2+
+x%5E2+-+%289%2F2%29%2Ax+%2B+81%2F16+=+-85%2F16+%2B+81%2F16+
+x%5E2+-+%289%2F2%29%2Ax+%2B+81%2F16+=+-4%2F16+
+%28+x+-+9%2F4+%29%5E2+=+%28+1%2F2%29%5E2+%2A+i%5E2+
Take the square root of both sides
+x+-+9%2F4+=+%281%2F2%29%2Ai+
+x+=+%28+9+%2B+2i+%29+%2F+4+
and, also
+x+=+%28+9+-+2i+%29+%2F+4+
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Here's the plot:
+graph%28+500%2C+500%2C+-2%2C+5%2C+-2%2C+8%2C+16x%5E2+-+72x+%2B+85+%29+
Since it doesn't contact the x-axis, there are no real roots