Question

Solve the equation k^2-6k=11 by completing the square

Answer 1

k = ±2√5 + 3

Explanation:

• k² - 6k + 9 = 11 + 9
• (k - 3)² = 20
• k - 3 = √20
• k - 3 = ±2√5
• k = ±2√5 + 3

Answer 2

`k=3+2\sqrt5\ or\ k=3-2\sqrt5`

Explanation:

`k^2-6k=11`

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Add one term in order to complete the square

`k^2-6k+(6*(1)/(2))^2=11+(6*(1)/(2))^2`

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Calculate

`k^2-6k+3^2=11+3^2`

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Factor the expression using
`a^2\pm 2ab+b^2=(a\pm b)^2`

`(k-3)^2=11+3^2`

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Calculate the power

`(k-3)^2=11+9`

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Calculate the sum or difference

`(k-3)^2=20`

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Split into two equations

`k-3=√(20)\ or\ k-3=-√(20)`

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Move variables to the left side of the equation:

`(k-3=√(20))`

`k=√(20)+3\\ k=2√(5)+3`

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Move variables to the left side of the equation:

`(k-3=-√(20))`

`k=√(20)+3\\ k=-2√(5)+3`

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So far:

`k=2√(5)+3\ or\ k=-2√(5)+3`

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Find the union of the solutions

`k=2√(5)+3\ or\ k=-2√(5)+3`

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I hope this helps you

:)