4x^2+380x+8400=1500

Simple and best practice solution for 4x^2+380x+8400=1500 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 4x^2+380x+8400=1500 equation: 


Simplifying
4x2 + 380x + 8400 = 1500

Reorder the terms:
8400 + 380x + 4x2 = 1500

Solving
8400 + 380x + 4x2 = 1500

Solving for variable 'x'.

Reorder the terms:
8400 + -1500 + 380x + 4x2 = 1500 + -1500

Combine like terms: 8400 + -1500 = 6900
6900 + 380x + 4x2 = 1500 + -1500

Combine like terms: 1500 + -1500 = 0
6900 + 380x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1725 + 95x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1725 + 95x + x2)' equal to zero and attempt to solve:

Simplifying
1725 + 95x + x2 = 0

Solving
1725 + 95x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1725' to each side of the equation.
1725 + 95x + -1725 + x2 = 0 + -1725

Reorder the terms:
1725 + -1725 + 95x + x2 = 0 + -1725

Combine like terms: 1725 + -1725 = 0
0 + 95x + x2 = 0 + -1725
95x + x2 = 0 + -1725

Combine like terms: 0 + -1725 = -1725
95x + x2 = -1725

The x term is 95x.  Take half its coefficient (47.5).
Square it (2256.25) and add it to both sides.

Add '2256.25' to each side of the equation.
95x + 2256.25 + x2 = -1725 + 2256.25

Reorder the terms:
2256.25 + 95x + x2 = -1725 + 2256.25

Combine like terms: -1725 + 2256.25 = 531.25
2256.25 + 95x + x2 = 531.25

Factor a perfect square on the left side:
(x + 47.5)(x + 47.5) = 531.25

Calculate the square root of the right side: 23.048861143

Break this problem into two subproblems by setting 
(x + 47.5) equal to 23.048861143 and -23.048861143.


Subproblem 1
x + 47.5 = 23.048861143

Simplifying
x + 47.5 = 23.048861143

Reorder the terms:
47.5 + x = 23.048861143

Solving
47.5 + x = 23.048861143

Solving for variable 'x'.

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

Add '-47.5' to each side of the equation.
47.5 + -47.5 + x = 23.048861143 + -47.5

Combine like terms: 47.5 + -47.5 = 0.0
0.0 + x = 23.048861143 + -47.5
x = 23.048861143 + -47.5

Combine like terms: 23.048861143 + -47.5 = -24.451138857
x = -24.451138857

Simplifying
x = -24.451138857


Subproblem 2
x + 47.5 = -23.048861143

Simplifying
x + 47.5 = -23.048861143

Reorder the terms:
47.5 + x = -23.048861143

Solving
47.5 + x = -23.048861143

Solving for variable 'x'.

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

Add '-47.5' to each side of the equation.
47.5 + -47.5 + x = -23.048861143 + -47.5

Combine like terms: 47.5 + -47.5 = 0.0
0.0 + x = -23.048861143 + -47.5
x = -23.048861143 + -47.5

Combine like terms: -23.048861143 + -47.5 = -70.548861143
x = -70.548861143

Simplifying
x = -70.548861143


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-24.451138857, -70.548861143}
Solution
x = {-24.451138857, -70.548861143}

See similar equations:

| 2w(3+4)=36+2w | | 12-3a=2+2a | | 3/4+1 | | 7x+6=111 | | 9=-17-3r | | 1x3/4 | | 9=17+-3r | | (X+3)+(x+5)=0 | | B/3=11 | | 11p+p= | | -22+4x=34 | | 11m-6-5m=-60 | | 5d+7e+10d+11e= | | 16x-5=5-16x | | (X-5)+6=0 | | 2x=1342.50 | | y=2x^3+8x^2 | | .35x+500=2.5x | | x^2-4/3x+4/9 | | -12x-4y=-4 | | 4x-x-6=21 | | 17-1/4x^2=12 | | 8=-3p+12 | | 88-12x=52 | | x+10=2x-4 | | -3(-9.5)+4y=2 | | 8p=2p+24 | | 80-8x=17-x | | -12x-4(-2)-12=-16 | | (2.5x)(3x)=30 | | (x-46)+x+(x-35)+1/2x=360 | | 3(-9.5)+2y=-44 |

Equations solver categories