6x^2+13x=42.25

Simple and best practice solution for 6x^2+13x=42.25 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 6x^2+13x=42.25 equation:


Simplifying
6x2 + 13x = 42.25

Reorder the terms:
13x + 6x2 = 42.25

Solving
13x + 6x2 = 42.25

Solving for variable 'x'.

Reorder the terms:
-42.25 + 13x + 6x2 = 42.25 + -42.25

Combine like terms: 42.25 + -42.25 = 0.00
-42.25 + 13x + 6x2 = 0.00

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

Divide each side by '6'.
-7.041666667 + 2.166666667x + x2 = 0.00

Move the constant term to the right:

Add '7.041666667' to each side of the equation.
-7.041666667 + 2.166666667x + 7.041666667 + x2 = 0.00 + 7.041666667

Reorder the terms:
-7.041666667 + 7.041666667 + 2.166666667x + x2 = 0.00 + 7.041666667

Combine like terms: -7.041666667 + 7.041666667 = 0.000000000
0.000000000 + 2.166666667x + x2 = 0.00 + 7.041666667
2.166666667x + x2 = 0.00 + 7.041666667

Combine like terms: 0.00 + 7.041666667 = 7.041666667
2.166666667x + x2 = 7.041666667

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 7.041666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 7.041666667 + 1.173611113

Combine like terms: 7.041666667 + 1.173611113 = 8.21527778
1.173611113 + 2.166666667x + x2 = 8.21527778

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 8.21527778

Calculate the square root of the right side: 2.866230587

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 2.866230587 and -2.866230587.

Subproblem 1

x + 1.083333334 = 2.866230587 Simplifying x + 1.083333334 = 2.866230587 Reorder the terms: 1.083333334 + x = 2.866230587 Solving 1.083333334 + x = 2.866230587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 2.866230587 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 2.866230587 + -1.083333334 x = 2.866230587 + -1.083333334 Combine like terms: 2.866230587 + -1.083333334 = 1.782897253 x = 1.782897253 Simplifying x = 1.782897253

Subproblem 2

x + 1.083333334 = -2.866230587 Simplifying x + 1.083333334 = -2.866230587 Reorder the terms: 1.083333334 + x = -2.866230587 Solving 1.083333334 + x = -2.866230587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -2.866230587 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -2.866230587 + -1.083333334 x = -2.866230587 + -1.083333334 Combine like terms: -2.866230587 + -1.083333334 = -3.949563921 x = -3.949563921 Simplifying x = -3.949563921

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.782897253, -3.949563921}

See similar equations:

| 2+12= | | 6x^2+13x+42.25=42.25 | | 233x^2-144x-89=0 | | 3x-6=x+14 | | -5x+3x-6=6 | | 5x-8(x+3)=4+x | | T^2-12t=-20 | | 3r^2+5r=6 | | 20+4a=4(a+5) | | -5n+19=-n+3(2n-7) | | x(x-3)=48 | | -5x+4=-4(x-5)-8 | | -34-2m=-5(-4+4m) | | (3y-2)(y-2)-y-3y-4= | | 2(1+7x)=8x-28 | | 2x-x=2 | | -12+3r=6(2r+7) | | X^2+23x-24=0 | | -19+3x=7+7(2-x) | | 5x+32=4-2x | | -8x-9+2x=3 | | 9x+6y=15(x+y) | | 7-5x=178 | | 7x-7=8x-2x | | -2+8(p-3)=-33+p | | [9x]=36 | | -2-8v=-2(7v+1) | | 2a+3b=5ab | | 2a^2+9a-5=0 | | -36-2v=7(v-5)-8v | | 5x-20=3x+40 | | -6(x-8)=34+8x |

Equations solver categories