Mathematics: What is the solution? 1/2x2-x+5=0

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What is the solution? 1/2x2-x+5=0 - id122504996918, honey66

Ответ:

robert7248

17.01.2022

Mathematics

Steps:

So for this, I will be completing the square. Firstly, subtract 5 on both sides of the equation:

$\frac{1}{2}x^2-x=-5$

Next, multiply both sides by 2:

x^2-2x=-10

Next, we want to make the left side of the equation a perfect square. To find the constant of the soon-to-be perfect square, divide the x coefficient by 2 and then square the quotient. Add the result to both sides of the equation:

-2 ÷ 2 = -1, (-1)² = 1

x^2-2x+1=-9

Next, factor the left side:

(x-1)^2=-9

Next, square root both sides of the equation:

$x-1=\pm \sqrt{-9}$

Next, remember that i = √-1 so factor that out on the right side of the equation:

$x-1=\pm i\sqrt{9}$

Lastly, add both sides by 1:

$x=1\pm i\sqrt{9}$

In short, your answer is $x=1\pm i\sqrt{9}$ , or the third option.

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What is the solution?
1/2x2-x+5=0

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