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Question
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
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Solution
Given:
`x - 18/x = 6`
Multiply both sides by x (assuming x ≠ 0):
x2 − 18 = 6x
x2 − 6x − 18 = 0
`x = (-(-6) +- sqrt((-6)^2 - 4(1)(-18)))/(2(1))`
`= (6+- sqrt(36+72))/2`
`= (6 +- sqrt108)/2`
`sqrt108`
= 10.39
`x = (6+- 10.39)/2`
First root:
`x = (6+10.39)/2`
`=16.39/2`
= 8.195
= 8.2
Second root:
`x = (6-10.39)/2`
`=(-4.39)/2`
= −2.195
= −2.2
x = 8.2 or x = −2.2
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