Quadratic equation?

Question

how would I solve:

(2x^2)+x=30

I got this far, is it right?

x(2x+1)-30=0

How would I solve it?

Answer 1

2x^2 + x = 30
2x^2 + x - 30 = 0

Now, either factor (if you can), or use quadratic formula.

I don't think it can be factored, so I'll use the quadratic formula.

a = 2
b = 1
c = -30

x = [-b +- sqrt (b^2 - 4ac)] / 2a
= [-1 +- sqrt (1^2 - 4*2*-30)] / 2(2)
= [-1 +- sqrt (1 + 240)] / 4
= [-1 +- sqrt 241] / 4
= [-1 +- 15.524] / 4
= -16.524 / 4 AND -14.524 / 4
= -4.131 AND -3.631

Answer 2

In the most general case, by completing the square.

2x^2 + x = 30
2x^2 + x - 30 =0
x^2 + 1/2*x - 15 = 0
(x^2 + 1/2*x + [1/4]^2) - 15 - (1/4)^2 = 0
(x+1/4)^2 = 15 + (1/4)^2
(x+1/4)^2 = 241/16
(x+1/4) = +- sqrt(241)/4
x = -1/4 +- sqrt(241)/4

Answer 3

(2x^2)+x=30
(2x^2)+x-30=0
use quadratic formula
a=2 b=1 c=-30

x = - b ± √ (b² - 4ac) / 2a
x = -1 ± √ (1² - 4(2)(-30) ) / 2(2)
x = -1 ± √ (241 ) / 4
x = [-1 ± 15.52]/ 4
x = = -4.13 OR x = -3.63

Answer 4

(2x^2)+x=30
2x^2+x-30=0
This doesn't seem to factor easily by eye-balling it.
Use the quadratic formula
x={-b+/- rt(b^2-4ac)} /2a
a=2, b=1, c=-30
x={-1+/- rt(1^2-4(2)(-30))} /4
x={-1+/-rt(1+240} /4
x={-1+/-rt(241)}/4
x={-1+15.52}/4 or {-1 -15.52}/4
x= 3.63 or -4.13
Something makes me think you typed in the problem incorrectly. If not, these are your answers

Answer 5

2x^2+x -30 = 0
Use quadratic equation
x = [ -1 +/- sqrt(1 + 240)]/4
x = [-1 +/- sqrt(241)]/4
x = -.25 + .25sqrt(241), and
x = -.25 - .25sqrt(241)

Answer 6

4x+x=30, 5x= 30, x =6

Answer 7

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