Question 46922
1) Solve:
{{{2x^2+2x = 4-x}}}  Rewrite the equation in the form:{{{ax^2+bx+c = 0}}}
{{{2x^2+3x-4 = 0}}} Use the quadratic formula to solve:
{{{x=(-b+-sqrt(b^2-4ac))/2a}}}

{{{x = (-3+-sqrt(3^2-4(2)(-4)))/2(2)}}}
{{{x = (-3+-sqrt(9+32))/4}}}
{{{x = (-3+-sqrt(41))/4}}}
{{{x = (-3+sqrt41)/4}}} = 0.85078...
{{{x = (-3-sqrt41)/4}}} = -2.35078...

2) Find the equation of the line passing through the points: (-2, 1) and (1, 2)

Use the point-slope form: y = mx+b.
Find the slope of the line: {{{m = (y2-y1)/(x2-x1)}}}
(-2, 1) = (x1, y1) and (1, 2) = (x2, y2)
{{{m = (2-1)/(1-(-2))}}}
{{{m = 1/3}}}

{{{y = (1/3)x + b}}} Now you need to find the value of b, the y-intercept. Substitute the x- and y-coordinates from either one of the two given points and solve for b. Using the second point (1, 2)
{{{2 = (1/3)(1) + b}}}
{{{2 = 1/3 + b}}} Subtract {{{1/3}}} from both sides of the equation.
{{{5/3 = b}}}
Now you can write the final equation.
{{{y = (1/3)x + 5/3}}}

3) When 3+4i is in the form a+bi, what is the value of a?

Compare the following:
3+4i
a+bi

a = 3