Question

Solving Quadratic Equations Walkthrough for 8bithelix

Answer 1

2x^2 + 16x = - 18

first step is to factor the left side such that the x^2 term has a coefficient of 1

2(x^2 + 8x) = -18

divide both sides by 2 to get

(x^2 + 8x) = -9

then, to "complete the square" this means we want to find a c term for x^2 + 8x that will make the left hand side a perfect square trinomial

to do this, we take the b coefficient (aka the coefficient of the x term, so 8, divide this by 2, square it --> you need to know this step by heart)

so that gives us (8/2)^2 = 16

adding this to both sides gives us

(x^2 + 8x + 16) = -9 + 16

then simplify to get

x^2 + 8x + 16 = 7

then, factor the left side, since it's a perfect square trinomial where (x+a)^2 = x^2 + 2ax + a^2, so:

(x+4)^2 = 7

taking the square root of this gives us

x + 4 = +/- sqrt(7) (it's a plus minus symbol indicating we are considering the positive and neg values of sqrt(7))

subtracting 4 from each side gives us

x = -4 +/- sqrt(7) = your answer

x^2 + 8x = 16 = 7

Answer 2

(sorry about that last line, idk how that got there)

Answer 3

anyway for 6, we just re-arrange the formula in the form ax^2 + bx + c = 0, so it's just adding 1 to each side

2x^2 - 5x + 1 = 0

now, if we compare the quadratic to the general form ax^2 + bx + c, we can see that a = 2, b = -5, and c = 1 (have to be careful about positive/negative signs here)

then plug them into the quadratic formula

Answer 4

this gives us

\[\frac{ -(-5 )±\sqrt{(-5)^{2}-4*1*2} }{ 2*2 }\]

Answer 5

\[\frac{ 5 )±\sqrt{25-8} }{ 4 }\]

Answer 6

then that gives us x = (5±sqrt(17))/4 = your answer

Answer 7

lmk if any steps are unclear

Answer 8

ok