0=-4+x+0.75x^2

Simple and best practice solution for 0=-4+x+0.75x^2 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 0=-4+x+0.75x^2 equation:


Simplifying
0 = -4 + x + 0.75x2

Solving
0 = -4 + x + 0.75x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + -1x + -0.75x2 = -4 + x + 0.75x2 + 4 + -1x + -0.75x2

Reorder the terms:
4 + -1x + -0.75x2 = -4 + 4 + x + -1x + 0.75x2 + -0.75x2

Combine like terms: -4 + 4 = 0
4 + -1x + -0.75x2 = 0 + x + -1x + 0.75x2 + -0.75x2
4 + -1x + -0.75x2 = x + -1x + 0.75x2 + -0.75x2

Combine like terms: x + -1x = 0
4 + -1x + -0.75x2 = 0 + 0.75x2 + -0.75x2
4 + -1x + -0.75x2 = 0.75x2 + -0.75x2

Combine like terms: 0.75x2 + -0.75x2 = 0.00
4 + -1x + -0.75x2 = 0.00

Begin completing the square.  Divide all terms by
-0.75 the coefficient of the squared term: 

Divide each side by '-0.75'.
-5.333333333 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 1.333333333x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 1.333333333x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 5.333333333
1.333333333x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
1.333333333x + x2 = 5.333333333

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 5.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 5.333333333 + 0.4444444442

Combine like terms: 5.333333333 + 0.4444444442 = 5.7777777772
0.4444444442 + 1.333333333x + x2 = 5.7777777772

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 5.7777777772

Calculate the square root of the right side: 2.40370085

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 2.40370085 and -2.40370085.

Subproblem 1

x + 0.6666666665 = 2.40370085 Simplifying x + 0.6666666665 = 2.40370085 Reorder the terms: 0.6666666665 + x = 2.40370085 Solving 0.6666666665 + x = 2.40370085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 2.40370085 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 2.40370085 + -0.6666666665 x = 2.40370085 + -0.6666666665 Combine like terms: 2.40370085 + -0.6666666665 = 1.7370341835 x = 1.7370341835 Simplifying x = 1.7370341835

Subproblem 2

x + 0.6666666665 = -2.40370085 Simplifying x + 0.6666666665 = -2.40370085 Reorder the terms: 0.6666666665 + x = -2.40370085 Solving 0.6666666665 + x = -2.40370085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -2.40370085 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -2.40370085 + -0.6666666665 x = -2.40370085 + -0.6666666665 Combine like terms: -2.40370085 + -0.6666666665 = -3.0703675165 x = -3.0703675165 Simplifying x = -3.0703675165

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7370341835, -3.0703675165}

See similar equations:

| X*2+15=11 | | 5m-10-4m-7=0 | | k-8/3=19/3 | | 1600-2Q= | | 3sin(2x+10)=2 | | -2.4+j=-1.8 | | 1700-2Q= | | -10(s+4)=-106 | | Z^4=6z^2+7 | | 5(y+-4)=35 | | 5y+4=35 | | 27=3(2x-3) | | 4-5x+20-6x=68 | | 8x+28=4(x+5) | | -36=8x-11x | | 8(x-10)=-92 | | (x-8)+x+(x+x-8)*0.75=70 | | (x^2+x)-(x+2)=0 | | (1,06²²-1)/(1,06²²,065) | | 7/2x=105 | | 2x+3(4+4)=2x+3(4) | | 422/x=9 | | -10x=10-10 | | Tan-1(8/3)=69.4 | | 2(4x-5)=-38 | | x^2+y^2+4x+5=0 | | 10+(x-1)10=200 | | log^3x=17 | | 6(3n-1)=4(n+4) | | 8+5y=8900 | | 15x-1=9-5x | | 3q=11q |

Equations solver categories