How do I solve 3x^2 + 2x -7 = 5x + 2
Trying to solve, haven't seen a problem like this in years.
3x^2 + 2x - 7 = 5x + 2
3x^2 + 2x - 7 - 5x - 2 = 5x + 2 - 5x - 2
3x^2 - 3x - 9 = 0
(3x^2 - 3x - 9) / 3 = 0 / 3
x^2 - x - 3 = 0
Use a method called "completing the square."
x^2 - x - 3 = 0
x^2 - x - 3 + 3 = 0 + 3
x^2 - x = 3
Add the square of 1/2 the x co-efficient: (-1/2)^2
x^2 - x + (-1/2)^2 = 3 + (-1/2)^2
x^2 - x + (-1/2)^2 = 3 + 0.25
x^2 - x + (-1/2)^2 = 3.25
Factor the left side.
(x - 0.5)(x - 0.5) = 3.25
Take the square root of both sides.
x - 0.5 = ±√3.25
x - 0.5 = ±1.80277
x - 0.5 + 0.5 = ±1.80277 + 0.5
x = ±1.80277 + 0.5
x = +1.80277 + 0.5 and x = -1.80277 + 0.5
x = +2.30277 and x = -1.30277
Check both values.
3x^2 + 2x - 7 = 5x + 2
3(2.30277)^2 + 2(2.30277) - 7 = 5(2.30277) + 2
3(5.302749) + 4.60554 - 7 = 11.51385 + 2
13.51378 ≈ 13.51385
3x^2 + 2x - 7 = 5x + 2
3(-1.30277)^2 + 2(-1.30277) - 7 = 5(-1.30277) + 2
3(1.6972) - 2.60554 - 7 = -6.51385 + 2
5.0916 - 2.60554 - 7 = -4.51385
-4.51394 ≈ -4.51385
Taking into account the rounding errors, they are approximately equal.