How do you solve $u^{2} - 4 u = 2 u + 35$ $u^2-4u=2u+35$ by completing the square?

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How do you solve $u^{2} - 4 u = 2 u + 35$ $u^2-4u=2u+35$ by completing the square?

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Answer 1 · 2017-02-20T20:58:45

$u = 3 + \sqrt{44}$ $u=3+sqrt(44)$ and $3 - \sqrt{44}$ $3-sqrt(44)$

Explanation:

First, subtract $2 u$ $2u$ on both sides.

$u^{2} - 6 u = 35$ $u^2-6u=35$

Now find ${(\frac{b}{2 a})}^{2}$ $(b/(2a))^2$ where $a$ $a$ is the coefficient in front of $u^{2}$ $u^2$ and $b$ $b$ is the coefficient in front of $u$ $u$ (so $b = - 6$ $b=-6$ and $a = 1$ $a=1$ in this case)

${(- \frac{6}{2 (1)})}^{2} = 9$ $(-6/(2(1)))^2=9$

Now, complete the square by adding both sides by 9.

$u^{2} - 6 u + 9 = 44$ $u^2-6u+9=44$

Rewrite the left side:

${(u - 3)}^{2} = 44$ $(u-3)^2=44$

Solve for u. Remember that taking the square root of both sides will give you a positive and negative number.

$(u - 3) = \sqrt{44}$ $(u-3)=sqrt(44)$ and $- \sqrt{44}$ $-sqrt(44)$

$u = 3 + \sqrt{44}$ $u=3+sqrt(44)$ and $3 - \sqrt{44}$ $3-sqrt(44)$

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How do you solve $u^{2} - 4 u = 2 u + 35$ $u^2-4u=2u+35$ by completing the square?

1 Answer

Explanation:

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How do you solve u2−4u=2u+35u^2-4u=2u+35 by completing the square?

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How do you solve $u^{2} - 4 u = 2 u + 35$ $u^2-4u=2u+35$ by completing the square?