0.5x^2+x-1=4

Simple and best practice solution for 0.5x^2+x-1=4 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 0.5x^2+x-1=4 equation: 


Simplifying
0.5x2 + x + -1 = 4

Reorder the terms:
-1 + x + 0.5x2 = 4

Solving
-1 + x + 0.5x2 = 4

Solving for variable 'x'.

Reorder the terms:
-1 + -4 + x + 0.5x2 = 4 + -4

Combine like terms: -1 + -4 = -5
-5 + x + 0.5x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-5 + x + 0.5x2 = 0

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

Divide each side by '0.5'.
-10 + 2x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 2x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2x + x2 = 0 + 10
2x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
2x + x2 = 10

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
2x + 0.25 + x2 = 10 + 0.25

Reorder the terms:
0.25 + 2x + x2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + 2x + x2 = 10.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + 0.5 = 3.201562119

Simplifying
x + 0.5 = 3.201562119

Reorder the terms:
0.5 + x = 3.201562119

Solving
0.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.201562119 + -0.5
x = 3.201562119 + -0.5

Combine like terms: 3.201562119 + -0.5 = 2.701562119
x = 2.701562119

Simplifying
x = 2.701562119


Subproblem 2
x + 0.5 = -3.201562119

Simplifying
x + 0.5 = -3.201562119

Reorder the terms:
0.5 + x = -3.201562119

Solving
0.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.201562119 + -0.5
x = -3.201562119 + -0.5

Combine like terms: -3.201562119 + -0.5 = -3.701562119
x = -3.701562119

Simplifying
x = -3.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.701562119, -3.701562119}

See similar equations:

| f(x)=2/5x-10 | | 9x^2+9=45 | | 8a+3y+5a-y= | | 3/4n=9= | | y=3x-n | | k=8k+26 | | C+c+c+c+c+cC= | | t^4-3t^2+4=0 | | 5x+4y-2x-3y= | | 8+x^3= | | 2/3x=46= | | x^4-20= | | 4h(-7+3h)=0 | | 4a+5b+a-b= | | -20y+15=2-16y+112 | | -16.1t^2+33t+10=0 | | 4a+5b+a+b= | | 13=t/7= | | y=6x^2+5x-4 | | m(a+2)+n(a+2)=0 | | 15b=10(b+10) | | (5c+4y)+(3x-3y)= | | 2x^3+8x^2-16=0 | | 2a+3b+5a+4b= | | 11x^3+27x^2+22x+6=0 | | -2x(2x+3)=-4 | | -2x(2x+3)=-4(x+1)-2 | | ln(6x+3)=4 | | 7y+5x=38 | | logx=4.5/5 | | -1/6×12 | | 9.7+3.1w-1.9= |

Equations solver categories