13x^2+32x-85=0

Simple and best practice solution for 13x^2+32x-85=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 13x^2+32x-85=0 equation:


Simplifying
13x2 + 32x + -85 = 0

Reorder the terms:
-85 + 32x + 13x2 = 0

Solving
-85 + 32x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-6.538461538 + 2.461538462x + x2 = 0

Move the constant term to the right:

Add '6.538461538' to each side of the equation.
-6.538461538 + 2.461538462x + 6.538461538 + x2 = 0 + 6.538461538

Reorder the terms:
-6.538461538 + 6.538461538 + 2.461538462x + x2 = 0 + 6.538461538

Combine like terms: -6.538461538 + 6.538461538 = 0.000000000
0.000000000 + 2.461538462x + x2 = 0 + 6.538461538
2.461538462x + x2 = 0 + 6.538461538

Combine like terms: 0 + 6.538461538 = 6.538461538
2.461538462x + x2 = 6.538461538

The x term is 2.461538462x.  Take half its coefficient (1.230769231).
Square it (1.514792900) and add it to both sides.

Add '1.514792900' to each side of the equation.
2.461538462x + 1.514792900 + x2 = 6.538461538 + 1.514792900

Reorder the terms:
1.514792900 + 2.461538462x + x2 = 6.538461538 + 1.514792900

Combine like terms: 6.538461538 + 1.514792900 = 8.053254438
1.514792900 + 2.461538462x + x2 = 8.053254438

Factor a perfect square on the left side:
(x + 1.230769231)(x + 1.230769231) = 8.053254438

Calculate the square root of the right side: 2.837825653

Break this problem into two subproblems by setting 
(x + 1.230769231) equal to 2.837825653 and -2.837825653.

Subproblem 1

x + 1.230769231 = 2.837825653 Simplifying x + 1.230769231 = 2.837825653 Reorder the terms: 1.230769231 + x = 2.837825653 Solving 1.230769231 + x = 2.837825653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.230769231' to each side of the equation. 1.230769231 + -1.230769231 + x = 2.837825653 + -1.230769231 Combine like terms: 1.230769231 + -1.230769231 = 0.000000000 0.000000000 + x = 2.837825653 + -1.230769231 x = 2.837825653 + -1.230769231 Combine like terms: 2.837825653 + -1.230769231 = 1.607056422 x = 1.607056422 Simplifying x = 1.607056422

Subproblem 2

x + 1.230769231 = -2.837825653 Simplifying x + 1.230769231 = -2.837825653 Reorder the terms: 1.230769231 + x = -2.837825653 Solving 1.230769231 + x = -2.837825653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.230769231' to each side of the equation. 1.230769231 + -1.230769231 + x = -2.837825653 + -1.230769231 Combine like terms: 1.230769231 + -1.230769231 = 0.000000000 0.000000000 + x = -2.837825653 + -1.230769231 x = -2.837825653 + -1.230769231 Combine like terms: -2.837825653 + -1.230769231 = -4.068594884 x = -4.068594884 Simplifying x = -4.068594884

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.607056422, -4.068594884}

See similar equations:

| 2x+95=5x+113 | | 15x+5=22x+4+120 | | 0.8n-4=3.2 | | 3s+19=94 | | 0.5y=0.4y | | 87=2w-13 | | p^9-64t^6= | | -3(x-5)=4(x+2) | | 0.6a=17a | | 8t-3=24 | | r+3=7 | | -7(-7-6v)=9+2v | | 48=5x-4.5 | | 9(6-5x)-9(8-7x)=72 | | 15m+74=149 | | 1.5d-16=8 | | x+(x-29.8)+(x+24.9)=195.5 | | 5d+9.2=19.7 | | (5/(x+6))-(1/(x-6))=2x/(x^2-36) | | 2w(2w-23)=-3w+10 | | 7.5b-2=28 | | 0.70x-0.60(x+20)=-0.40(20) | | 16c-6.5=9.5 | | x+2x=123 | | 0.39(x+50)+0.36(x+45)=35.55 | | 0.39(x+50)+0.36(x+45)=53.55 | | 7(5x-5)=37-x | | 2c-3.1=1.7 | | 2t-3=25 | | 0.444x=-0.142 | | y/3+8 | | 3a-5=1 |

Equations solver categories