-16x^2+28x+32=0

Simple and best practice solution for -16x^2+28x+32=0 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+28x+32=0 equation: 


Simplifying
-16x2 + 28x + 32 = 0

Reorder the terms:
32 + 28x + -16x2 = 0

Solving
32 + 28x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 7x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + 7x + -4x2)' equal to zero and attempt to solve:

Simplifying
8 + 7x + -4x2 = 0

Solving
8 + 7x + -4x2 = 0

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

Divide each side by '-4'.
-2 + -1.75x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -1.75x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -1.75x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1.75x + x2 = 0 + 2
-1.75x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1.75x + x2 = 2

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 2 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 2 + 0.765625

Combine like terms: 2 + 0.765625 = 2.765625
0.765625 + -1.75x + x2 = 2.765625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 2.765625

Calculate the square root of the right side: 1.663016837

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.663016837 and -1.663016837.


Subproblem 1
x + -0.875 = 1.663016837

Simplifying
x + -0.875 = 1.663016837

Reorder the terms:
-0.875 + x = 1.663016837

Solving
-0.875 + x = 1.663016837

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.663016837 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.663016837 + 0.875
x = 1.663016837 + 0.875

Combine like terms: 1.663016837 + 0.875 = 2.538016837
x = 2.538016837

Simplifying
x = 2.538016837


Subproblem 2
x + -0.875 = -1.663016837

Simplifying
x + -0.875 = -1.663016837

Reorder the terms:
-0.875 + x = -1.663016837

Solving
-0.875 + x = -1.663016837

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.663016837 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.663016837 + 0.875
x = -1.663016837 + 0.875

Combine like terms: -1.663016837 + 0.875 = -0.788016837
x = -0.788016837

Simplifying
x = -0.788016837


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.538016837, -0.788016837}
Solution
x = {2.538016837, -0.788016837}

See similar equations:

| 14+4x=0-3x | | (1+x)+(x/2)+(2x+6)+(x+3)+(x+5)=0 | | 4x^2+380x+8400=1500 | | 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 |

Equations solver categories