2x^2+14x+23=0

Simple and best practice solution for 2x^2+14x+23=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+14x+23=0 equation:


Simplifying
2x2 + 14x + 23 = 0

Reorder the terms:
23 + 14x + 2x2 = 0

Solving
23 + 14x + 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'.
11.5 + 7x + x2 = 0

Move the constant term to the right:

Add '-11.5' to each side of the equation.
11.5 + 7x + -11.5 + x2 = 0 + -11.5

Reorder the terms:
11.5 + -11.5 + 7x + x2 = 0 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + 7x + x2 = 0 + -11.5
7x + x2 = 0 + -11.5

Combine like terms: 0 + -11.5 = -11.5
7x + x2 = -11.5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -11.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -11.5 + 12.25

Combine like terms: -11.5 + 12.25 = 0.75
12.25 + 7x + x2 = 0.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(x + 3.5) equal to 0.866025404 and -0.866025404.

Subproblem 1

x + 3.5 = 0.866025404 Simplifying x + 3.5 = 0.866025404 Reorder the terms: 3.5 + x = 0.866025404 Solving 3.5 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 0.866025404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 0.866025404 + -3.5 x = 0.866025404 + -3.5 Combine like terms: 0.866025404 + -3.5 = -2.633974596 x = -2.633974596 Simplifying x = -2.633974596

Subproblem 2

x + 3.5 = -0.866025404 Simplifying x + 3.5 = -0.866025404 Reorder the terms: 3.5 + x = -0.866025404 Solving 3.5 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -0.866025404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -0.866025404 + -3.5 x = -0.866025404 + -3.5 Combine like terms: -0.866025404 + -3.5 = -4.366025404 x = -4.366025404 Simplifying x = -4.366025404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.633974596, -4.366025404}

See similar equations:

| 542=-24x+86y | | 3(55)-105=x | | 3x-105+2x+10=180 | | -7x+4=9x+6 | | X^2+12+33=0 | | 4x-62=-x-2 | | 9x-67=-6x+8 | | x-35=8x | | 2x+46=5x+7 | | -x+4=5x+9 | | 26+15x=11+18x | | x+98=-5x+8 | | -45=5(a+-3) | | 3(-7k+2)=-(-6-5k)+2k | | 7y-3=53 | | 4(6t-7)=31+8 | | -7x-85=4x+3 | | (b^2-b-6/2b)/(b^2-4/b^2) | | 14x-(45)=90 | | 4x-50=8x-6 | | -5x-40=3x | | 8*23= | | (7a/10)/(5/21) | | -r+3(8+3r)=7 | | 11/6+5 | | (2/3)-(5/7) | | 8+5(-5x+6x)+23= | | 2/3-5/7 | | 1x+4=2x+5 | | -3500+1800x=30 | | x^2-2x-3*sqrt(x)=0 | | 6-1.1= |

Equations solver categories