3x^2+7x=420

Simple and best practice solution for 3x^2+7x=420 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 3x^2+7x=420 equation:


Simplifying
3x2 + 7x = 420

Reorder the terms:
7x + 3x2 = 420

Solving
7x + 3x2 = 420

Solving for variable 'x'.

Reorder the terms:
-420 + 7x + 3x2 = 420 + -420

Combine like terms: 420 + -420 = 0
-420 + 7x + 3x2 = 0

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

Divide each side by '3'.
-140 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 2.333333333x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + 2.333333333x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 2.333333333x + x2 = 0 + 140
2.333333333x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
2.333333333x + x2 = 140

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 140 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 140 + 1.361111112

Combine like terms: 140 + 1.361111112 = 141.361111112
1.361111112 + 2.333333333x + x2 = 141.361111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 141.361111112

Calculate the square root of the right side: 11.889537885

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 11.889537885 and -11.889537885.

Subproblem 1

x + 1.166666667 = 11.889537885 Simplifying x + 1.166666667 = 11.889537885 Reorder the terms: 1.166666667 + x = 11.889537885 Solving 1.166666667 + x = 11.889537885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 11.889537885 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 11.889537885 + -1.166666667 x = 11.889537885 + -1.166666667 Combine like terms: 11.889537885 + -1.166666667 = 10.722871218 x = 10.722871218 Simplifying x = 10.722871218

Subproblem 2

x + 1.166666667 = -11.889537885 Simplifying x + 1.166666667 = -11.889537885 Reorder the terms: 1.166666667 + x = -11.889537885 Solving 1.166666667 + x = -11.889537885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -11.889537885 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -11.889537885 + -1.166666667 x = -11.889537885 + -1.166666667 Combine like terms: -11.889537885 + -1.166666667 = -13.056204552 x = -13.056204552 Simplifying x = -13.056204552

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.722871218, -13.056204552}

See similar equations:

| -84=-4x-2(4x+12) | | 4x^2+5x=440 | | 56+(-7)=63 | | 11=h-4 | | 4yard= | | 21.2(.65)/c | | (9+17)+a=59 | | 4yards=124inches | | 14+c=16 | | (2x+6)+34=180 | | 7x-3(6x+13)=38 | | 70kg*9.8m/s2 | | (2x-3)+(71)=180 | | 750=wl | | 11-3=8x+9 | | sinx=7/23 | | -4(3-x)=2(x+8) | | 80=2l | | 12/30=6/n | | 92=6h+12-2h+4 | | 3x-8-2x=7 | | 6n^2+42n+36=0 | | 3^x=1/243 | | 6g=21 | | 14x^2+38x+20=0 | | x-2*x-2=0 | | 5(r+6)=-5(r+3) | | w-(-3)=2 | | 198=3x-3(-7x-2) | | 7(x-5)=-4x-13 | | 8-f=6f-6 | | 198=3x-3 |

Equations solver categories