Question

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

Answer 1

Answer:

k = ±2√5 + 3

Step-by-step explanation:

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

Answer 2

Answer:

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

Step-by-step explanation:

$k^2-6k=11$

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Add one term in order to complete the square

$k^2-6k+(6\times\frac{1}{2})^2=11+(6\times\frac{1}{2})^2$

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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

$k-3=\sqrt{20}\ or\ k-3=-\sqrt{20}$

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Move variables to the left side of the equation:

                                 $(k-3=\sqrt{20})$

$k=\sqrt{20}+3\\ k=2\sqrt{5}+3$

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Move variables to the left side of the equation:

                               $(k-3=-\sqrt{20})$

$k=\sqrt{20}+3\\ k=-2\sqrt{5}+3$

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So far:

$k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3$

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Find the union of the solutions

$k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3$

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I hope this helps you

:)