Question

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

Answer 1

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:

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

Answer:

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

Answer 2

The solution to the quadratic equation given is 1 + 3i and 1 -3i

Given the quadratic expression $\frac{1}{2} x^2 -x + 5 = 0$

Multiplying through by 2:

$x^2 -2x + 10 =0$

Using the general formula:

x = -(-2)±√(-2)² -4(10)/2

x = 2±√4 -40/2

x = 2±√-36/2

x = 2±6i/2

x = 2+6i/2 and 2-6i/2

x = 1 + 3i and 1 -3i

Hence the solution to the quadratic equation given is 1 + 3i and 1 -3i

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