-16x^2+120x+400=300

Simple and best practice solution for -16x^2+120x+400=300 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 -16x^2+120x+400=300 equation: 


Simplifying
-16x2 + 120x + 400 = 300

Reorder the terms:
400 + 120x + -16x2 = 300

Solving
400 + 120x + -16x2 = 300

Solving for variable 'x'.

Reorder the terms:
400 + -300 + 120x + -16x2 = 300 + -300

Combine like terms: 400 + -300 = 100
100 + 120x + -16x2 = 300 + -300

Combine like terms: 300 + -300 = 0
100 + 120x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + 30x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25 + 30x + -4x2)' equal to zero and attempt to solve:

Simplifying
25 + 30x + -4x2 = 0

Solving
25 + 30x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-6.25 + -7.5x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -7.5x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -7.5x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -7.5x + x2 = 0 + 6.25
-7.5x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-7.5x + x2 = 6.25

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 6.25 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 6.25 + 14.0625

Combine like terms: 6.25 + 14.0625 = 20.3125
14.0625 + -7.5x + x2 = 20.3125

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 20.3125

Calculate the square root of the right side: 4.506939094

Break this problem into two subproblems by setting 
(x + -3.75) equal to 4.506939094 and -4.506939094.


Subproblem 1
x + -3.75 = 4.506939094

Simplifying
x + -3.75 = 4.506939094

Reorder the terms:
-3.75 + x = 4.506939094

Solving
-3.75 + x = 4.506939094

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 4.506939094 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 4.506939094 + 3.75
x = 4.506939094 + 3.75

Combine like terms: 4.506939094 + 3.75 = 8.256939094
x = 8.256939094

Simplifying
x = 8.256939094


Subproblem 2
x + -3.75 = -4.506939094

Simplifying
x + -3.75 = -4.506939094

Reorder the terms:
-3.75 + x = -4.506939094

Solving
-3.75 + x = -4.506939094

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -4.506939094 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -4.506939094 + 3.75
x = -4.506939094 + 3.75

Combine like terms: -4.506939094 + 3.75 = -0.756939094
x = -0.756939094

Simplifying
x = -0.756939094


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.256939094, -0.756939094}
Solution
x = {8.256939094, -0.756939094}

See similar equations:

| 65+15p=35 | | (k-3)x^2-(3k-2)x+3k+1=0 | | 3(3.8+-0.6y)+y=9 | | .05=1.82/x | | -2y=4y-42 | | 64=-2(m+7)+m | | 63+7x=84+4x | | 4x-6x=12-20-5x | | 7x/2_x=0 | | 475+40+28h=601 | | 5x-3(4x-13)=81 | | 5(3.8+-0.6y)+3y=19 | | 16=4(v+1) | | 12n-9+2n-n=-87 | | 2w^2+6=-7w | | 5x-3(-5x-9)=127 | | 40=5ln(x-2)+6 | | 2w^2+6+7w=0 | | 7.95+4.35=60 | | -3x-6(3x+14)=147 | | -6x+4-3+x=11 | | 12-3=7(n-4)+5n | | (-14)(0.22)+(-16)(0.65)=(-18)(0.13) | | 8x+7y-3x= | | -2x-2(7x-16)=-10 | | 4y+4=-2x | | 14-4X=5=X/2 | | y-0.65y=3500 | | 7x+25*2=127 | | 40=2mxn | | 0.1x+x=2.75 | | 4x+32x+1=0 |

Equations solver categories