3h^2+17h=10

Simple and best practice solution for 3h^2+17h=10 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 3h^2+17h=10 equation: 


Simplifying
3h2 + 17h = 10

Reorder the terms:
17h + 3h2 = 10

Solving
17h + 3h2 = 10

Solving for variable 'h'.

Reorder the terms:
-10 + 17h + 3h2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 17h + 3h2 = 0

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

Divide each side by '3'.
-3.333333333 + 5.666666667h + h2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 5.666666667h + 3.333333333 + h2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 5.666666667h + h2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 5.666666667h + h2 = 0 + 3.333333333
5.666666667h + h2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
5.666666667h + h2 = 3.333333333

The h term is 5.666666667h.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667h + 8.027777782 + h2 = 3.333333333 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667h + h2 = 3.333333333 + 8.027777782

Combine like terms: 3.333333333 + 8.027777782 = 11.361111115
8.027777782 + 5.666666667h + h2 = 11.361111115

Factor a perfect square on the left side:
(h + 2.833333334)(h + 2.833333334) = 11.361111115

Calculate the square root of the right side: 3.370624737

Break this problem into two subproblems by setting 
(h + 2.833333334) equal to 3.370624737 and -3.370624737.


Subproblem 1
h + 2.833333334 = 3.370624737

Simplifying
h + 2.833333334 = 3.370624737

Reorder the terms:
2.833333334 + h = 3.370624737

Solving
2.833333334 + h = 3.370624737

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + h = 3.370624737 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + h = 3.370624737 + -2.833333334
h = 3.370624737 + -2.833333334

Combine like terms: 3.370624737 + -2.833333334 = 0.537291403
h = 0.537291403

Simplifying
h = 0.537291403


Subproblem 2
h + 2.833333334 = -3.370624737

Simplifying
h + 2.833333334 = -3.370624737

Reorder the terms:
2.833333334 + h = -3.370624737

Solving
2.833333334 + h = -3.370624737

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + h = -3.370624737 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + h = -3.370624737 + -2.833333334
h = -3.370624737 + -2.833333334

Combine like terms: -3.370624737 + -2.833333334 = -6.203958071
h = -6.203958071

Simplifying
h = -6.203958071


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.537291403, -6.203958071}

See similar equations:

| 3h^2+17h= | | 2(x+6)-x=4 | | d^2-4d-60=0 | | 3x+2y+x=x+6 | | 2(3a-1)-5a=8-2 | | 1/35×5 | | 3(b-2)-2(b-4)=5(b+1) | | 295=192-w | | x+x+85+x+20=180 | | -3(x-3)+4x=8-4 | | y-120=2x | | n^2-14n-22=0 | | 25=1/3B5 | | 3d^2+8d+5= | | 42=13y-y^2 | | 11p-11q+5-11p-8= | | x+x+90+x+15=180 | | -(x+6)+2x-3=2 | | 4(v+5)-2v=16 | | 3-y=290 | | e+8= | | 5(x+7)=7X+9 | | 2x+46=6x-5 | | 5(x+7)=7X+10 | | 3(7-x)=-3 | | 13x+8y=-40 | | -0.5=2n-3(x-0.5) | | 2x^2-13x-3=4 | | 9/2=3/x | | 6(-6+4x)=228 | | 9/2=3/3 | | 4cos^3(x)+4cos(x)=0 |

Equations solver categories