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Solve each of the quadratic equations:

1. [tex]\(3x = 0.5x^2\)[/tex]
A. [tex]\(x = -6\)[/tex] or [tex]\(x = 0\)[/tex]
B. [tex]\(x = -4\)[/tex] or [tex]\(x = 3\)[/tex]
C. [tex]\(x = -2\)[/tex] or [tex]\(x = 1.5\)[/tex]
D. [tex]\(x = 0\)[/tex] or [tex]\(x = 6\)[/tex]

2. [tex]\(0 = 5x^2 - 2x + 6\)[/tex]
A. [tex]\(x = \frac{1 + 3i}{2}\)[/tex]
B. [tex]\(x = \frac{1 \pm \sqrt{11}}{5}\)[/tex]
C. [tex]\(x = \frac{1 \pm i \sqrt{29}}{5}\)[/tex]



Answer :

GinnyAnswer
Let's solve the quadratic equation step by step:

Given quadratic equation:
[tex]\[ 3x = 0.5x^2 \][/tex]

First, we need to rearrange it to standard form [tex]\( ax^2 + bx + c = 0 \)[/tex]:

1. Rearrange the equation:
[tex]\[ 0.5x^2 - 3x = 0 \][/tex]

2. Factor out the common term:
[tex]\[ x(0.5x - 3) = 0 \][/tex]

This gives us two potential solutions from the factored equation:
[tex]\[ x = 0 \][/tex]
or
[tex]\[ 0.5x - 3 = 0 \][/tex]

3. Solve the second equation for [tex]\( x \)[/tex]:
[tex]\[ 0.5x - 3 = 0 \][/tex]
Add 3 to both sides:
[tex]\[ 0.5x = 3 \][/tex]
Divide both sides by 0.5:
[tex]\[ x = \frac{3}{0.5} \][/tex]
[tex]\[ x = 6 \][/tex]

So, the solutions to the original quadratic equation are:
[tex]\[ x = 0 \][/tex]
and
[tex]\[ x = 6 \][/tex]

Therefore, the correct solution is:
[tex]\[ x = 0 \text{ or } x = 6 \][/tex]

So, among the choices given, the correct one is:
[tex]\[ x=0 \text{ or } x=6 \][/tex]

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