7n^2+19n-14=0

Simple and best practice solution for 7n^2+19n-14=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 7n^2+19n-14=0 equation:


Simplifying
7n2 + 19n + -14 = 0

Reorder the terms:
-14 + 19n + 7n2 = 0

Solving
-14 + 19n + 7n2 = 0

Solving for variable 'n'.

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

Divide each side by '7'.
-2 + 2.714285714n + n2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.714285714n + 2 + n2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.714285714n + n2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.714285714n + n2 = 0 + 2
2.714285714n + n2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.714285714n + n2 = 2

The n term is 2.714285714n.  Take half its coefficient (1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
2.714285714n + 1.841836734 + n2 = 2 + 1.841836734

Reorder the terms:
1.841836734 + 2.714285714n + n2 = 2 + 1.841836734

Combine like terms: 2 + 1.841836734 = 3.841836734
1.841836734 + 2.714285714n + n2 = 3.841836734

Factor a perfect square on the left side:
(n + 1.357142857)(n + 1.357142857) = 3.841836734

Calculate the square root of the right side: 1.96006039

Break this problem into two subproblems by setting 
(n + 1.357142857) equal to 1.96006039 and -1.96006039.

Subproblem 1

n + 1.357142857 = 1.96006039 Simplifying n + 1.357142857 = 1.96006039 Reorder the terms: 1.357142857 + n = 1.96006039 Solving 1.357142857 + n = 1.96006039 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + n = 1.96006039 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + n = 1.96006039 + -1.357142857 n = 1.96006039 + -1.357142857 Combine like terms: 1.96006039 + -1.357142857 = 0.602917533 n = 0.602917533 Simplifying n = 0.602917533

Subproblem 2

n + 1.357142857 = -1.96006039 Simplifying n + 1.357142857 = -1.96006039 Reorder the terms: 1.357142857 + n = -1.96006039 Solving 1.357142857 + n = -1.96006039 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + n = -1.96006039 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + n = -1.96006039 + -1.357142857 n = -1.96006039 + -1.357142857 Combine like terms: -1.96006039 + -1.357142857 = -3.317203247 n = -3.317203247 Simplifying n = -3.317203247

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.602917533, -3.317203247}

See similar equations:

| 15x+31y=-3 | | 10y-6=7y | | (16y)(16y)-8y=0 | | 2.5k^2-7.5k+1.25=0 | | Y=p^2-14pq+33q^2 | | 8/3s=-9-(-7) | | 2(16y)-8y=0 | | 2x+4(-x+15)=42 | | -2(x+13)=-6 | | 2x(4x^2y+xy^2+5xy)= | | hw/6h^2w^4 | | (5x-14)+(3y-20)=180 | | 5/x=-5 | | 25x^3+4x=0 | | 3s^2(4s^2-7s)= | | 25x^3+-4x=0 | | 2x-3-2=5 | | (2x+60)=6x | | 4(a-4)+5a=-22 | | 3a(4a+5)= | | (-3m^5n^2)(2m^4n)= | | (80.5+79.5+x)/3=70 | | 2x-6=10x-8 | | 2x+6+38=180 | | X+3-4=0 | | 2n^3/2n^2 | | 4(2x)+3x=72 | | 4x-9x=176 | | .15/8*2/45 | | (4x^3y^2)(8x^2y)= | | 3/412/16 | | 2(2x-6)=8 |

Equations solver categories