P is the midpoint of DE¯¯¯¯¯DE¯ , DP=3x+2DP=3x+2, and DE=10x−12DE=10x−12. What is the length of DP¯¯¯¯¯DP¯ ?
2 answers:
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Step One
Begin by getting one side of the question equal to zero.
32x -4 = 4x^2 + 60 Add - 32x + 4 from both sides.
0 = 4x^2 + 60 - 32x + 4 Collect like terms.
0 = 4x^2 - 32x + 64
Step Two
For this question, you could divide both sides by 4. It just makes the steps later on easier.
0 = x^2 - 8x + 16
Step Three
Calculate the discriminate.
The discriminate is b^2 - 4*a*c
a = 1; b = -8; c = 16
b^2 - 4*a*c = (-8)^2 - 4*(1)(16) = 64 - 64 = 0
There is only 1 root. It is real and it is rational.
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