2n^2-3n-21=0

Simple and best practice solution for 2n^2-3n-21=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 2n^2-3n-21=0 equation:


Simplifying
2n2 + -3n + -21 = 0

Reorder the terms:
-21 + -3n + 2n2 = 0

Solving
-21 + -3n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
-10.5 + -1.5n + n2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -1.5n + 10.5 + n2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -1.5n + n2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -1.5n + n2 = 0 + 10.5
-1.5n + n2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-1.5n + n2 = 10.5

The n term is -1.5n.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5n + 0.5625 + n2 = 10.5 + 0.5625

Reorder the terms:
0.5625 + -1.5n + n2 = 10.5 + 0.5625

Combine like terms: 10.5 + 0.5625 = 11.0625
0.5625 + -1.5n + n2 = 11.0625

Factor a perfect square on the left side:
(n + -0.75)(n + -0.75) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(n + -0.75) equal to 3.326033674 and -3.326033674.

Subproblem 1

n + -0.75 = 3.326033674 Simplifying n + -0.75 = 3.326033674 Reorder the terms: -0.75 + n = 3.326033674 Solving -0.75 + n = 3.326033674 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + n = 3.326033674 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + n = 3.326033674 + 0.75 n = 3.326033674 + 0.75 Combine like terms: 3.326033674 + 0.75 = 4.076033674 n = 4.076033674 Simplifying n = 4.076033674

Subproblem 2

n + -0.75 = -3.326033674 Simplifying n + -0.75 = -3.326033674 Reorder the terms: -0.75 + n = -3.326033674 Solving -0.75 + n = -3.326033674 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + n = -3.326033674 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + n = -3.326033674 + 0.75 n = -3.326033674 + 0.75 Combine like terms: -3.326033674 + 0.75 = -2.576033674 n = -2.576033674 Simplifying n = -2.576033674

Solution

The solution to the problem is based on the solutions from the subproblems. n = {4.076033674, -2.576033674}

See similar equations:

| -(7y+4)-(-6y-8)=4 | | 3(x+9)=8x+8-5x+19 | | 8h=6+30 | | 4ln(5x)=12 | | -7(7y+4)-(-6y-8)=4 | | 3x-8=2x+16 | | 1-3n=3.5+9n | | .6h=12 | | 10-5n=9-3n | | (V-10)(6v-1)= | | 2x-2=2(x+3) | | (3v-5)(2v-2)= | | 5(2x-8)-6=5(x-4)+9 | | 7A^3+16A^2-15A= | | .5(x+200)=.58x-476 | | -5(2p+3)= | | -6x+25=-17 | | 14x^2=25x+25 | | -x^2+5x-18=0 | | -3x+2=-13 | | -3(4m+4)= | | 16x^2-13x-4=0 | | 0.06(x+9)=0.03(2x+9)+0.27 | | a^2q^2-49=0 | | 9-2x=3x+9 | | 5(4.2j-2.4)=1.5(8j-4) | | 5y-10x=20 | | 3(x+4)=8x+4-5x+8 | | 9x-6=9(x+2) | | 5(4.2j-2.4)=1.5(8y-4) | | 25y-40=10y-20 | | 3x-40=2x |

Equations solver categories