2x^2+29x+78=0

Simple and best practice solution for 2x^2+29x+78=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 2x^2+29x+78=0 equation:


Simplifying
2x2 + 29x + 78 = 0

Reorder the terms:
78 + 29x + 2x2 = 0

Solving
78 + 29x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
39 + 14.5x + x2 = 0

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 14.5x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + 14.5x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 14.5x + x2 = 0 + -39
14.5x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
14.5x + x2 = -39

The x term is 14.5x.  Take half its coefficient (7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
14.5x + 52.5625 + x2 = -39 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = -39 + 52.5625

Combine like terms: -39 + 52.5625 = 13.5625
52.5625 + 14.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + 7.25) equal to 3.682729966 and -3.682729966.

Subproblem 1

x + 7.25 = 3.682729966 Simplifying x + 7.25 = 3.682729966 Reorder the terms: 7.25 + x = 3.682729966 Solving 7.25 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 3.682729966 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 3.682729966 + -7.25 x = 3.682729966 + -7.25 Combine like terms: 3.682729966 + -7.25 = -3.567270034 x = -3.567270034 Simplifying x = -3.567270034

Subproblem 2

x + 7.25 = -3.682729966 Simplifying x + 7.25 = -3.682729966 Reorder the terms: 7.25 + x = -3.682729966 Solving 7.25 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -3.682729966 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -3.682729966 + -7.25 x = -3.682729966 + -7.25 Combine like terms: -3.682729966 + -7.25 = -10.932729966 x = -10.932729966 Simplifying x = -10.932729966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.567270034, -10.932729966}

See similar equations:

| 0.8×1/5 | | 7n-13=21 | | 18-4x=-3 | | 5/12x=-4/36 | | 5x-30y=15 | | 3x^2+18x-11=154 | | -5(4n-8)=6(-4n-4) | | -90+(2)= | | 1/6x^3-7/48x^2 | | X^2-42=90 | | 4x+39=5x-3 | | 68=(20x+50)+2 | | 9x-24=4x+6 | | -11/20=-x-11/16 | | 7x-14=x-8 | | 5+2a-3=5/11 | | 5+3=58 | | -20k^2+34k=3k-27 | | 12-15+24+1=45 | | 7(8x-2)+6(x+4)=-52 | | p+0.05p=52.5 | | 2m^2=9m+14 | | -26=-2m | | 0.5q=0.6 | | 2/P-2T=1/3 | | 6.66x+10=-12 | | 12(-2a-9)+3=-9(2+12a)-3a | | -16+-3=19 | | 6z+1=13-3z | | -3x+7(x+5)=-1 | | 53-32j=97 | | 3x^2+18-11=154 |

Equations solver categories