2n^2+10n=-7

Simple and best practice solution for 2n^2+10n=-7 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 2n^2+10n=-7 equation:


Simplifying
2n2 + 10n = -7

Reorder the terms:
10n + 2n2 = -7

Solving
10n + 2n2 = -7

Solving for variable 'n'.

Reorder the terms:
7 + 10n + 2n2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 10n + 2n2 = 0

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

Divide each side by '2'.
3.5 + 5n + n2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 5n + -3.5 + n2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 5n + n2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 5n + n2 = 0 + -3.5
5n + n2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
5n + n2 = -3.5

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = -3.5 + 6.25

Reorder the terms:
6.25 + 5n + n2 = -3.5 + 6.25

Combine like terms: -3.5 + 6.25 = 2.75
6.25 + 5n + n2 = 2.75

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(n + 2.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

n + 2.5 = 1.658312395 Simplifying n + 2.5 = 1.658312395 Reorder the terms: 2.5 + n = 1.658312395 Solving 2.5 + n = 1.658312395 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 1.658312395 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 1.658312395 + -2.5 n = 1.658312395 + -2.5 Combine like terms: 1.658312395 + -2.5 = -0.841687605 n = -0.841687605 Simplifying n = -0.841687605

Subproblem 2

n + 2.5 = -1.658312395 Simplifying n + 2.5 = -1.658312395 Reorder the terms: 2.5 + n = -1.658312395 Solving 2.5 + n = -1.658312395 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -1.658312395 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -1.658312395 + -2.5 n = -1.658312395 + -2.5 Combine like terms: -1.658312395 + -2.5 = -4.158312395 n = -4.158312395 Simplifying n = -4.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.841687605, -4.158312395}

See similar equations:

| 1(a-3)=4(a+7)-2a | | x^2/25=16 | | 4+-2x+6=-4 | | .2x+.5y=.32(x+y) | | W-7=3/5 | | (2x-5)-8=-6 | | 1/3(3328) | | 2+y=-3y | | 20x^3/4x^2-12x | | (8a^8b^6)/10a^7b^6 | | 3a+4b=114 | | 5q+2p+4=3q-8 | | 2(5x-2)=x+5 | | 6x-2x+3=-5 | | T^2-12t+36=9 | | 5(2p+4)=-2p-16 | | -3/4=1/8x | | (6a^4b^9)(-4x^2y^6)= | | k=2x+4 | | 2/3×6/5= | | 2x+3x-1=7 | | 26-3m=-4(m-5) | | x^2=169/25 | | -.4=g/3-.9 | | .2x+.5y=.32z | | 5x-13x+2x=(-70)+x | | x+10-3=6 | | 1/3(468) | | -3xy=-23 | | 2+y=-3y-4 | | 4+3(4+x)=-20-3x | | y.23=12 |

Equations solver categories