2x^2+2x-6=0? kinda complicated?

Question

solve using quadratic formula

Answer 1

2x² + 2x - 6 = 0

First, I would divide everything by 2:

x² + x - 3 = 0

a = 1

b = 1

c = -3

x = { -b ± sqrt( b² + 4ac ) } / 2a

x = { -1 ± sqrt( 1 + 12 ) } / 2

x = { -1 ± sqrt( 13 ) } / 2

If you want an approximation:

x ≈ 1.3028

x ≈ -2.3028

Answer 2

do you know the song?? the opposite of b, plus or minus square root, b squared minus 4ac, all over 2a. just plug in the numbers. it's not too hard.

Answer 3

To use the quadratic formula, the equation needs to be in the standard form:

ax^2 + bx + c = 0

Now, it should be clear that a = 2, b = 2, and c = -6.  These values can now be plugged into the quadratic equation to solve the problem:

x = [-b +/-√(b^2 - 4ac)] / 2a

x = [-2 +/-√(2^2 - 4(2)(-6))] / 2(2)

x = [-2 +/-√(4 - (-48))] / 4

x = [-2 +/-√52] / 4

Knowing that 52 = 4 * 13, we can simplify √52

√52 = √(4*13) = (√4)(√13) = 2√13

So, x is either (-2 + 2√13)/4 or (-2 - 2√13)/4

x = -1/2 + (√13)/2

x = -1/2 - (√13)/2