0.5x^2=3x+0.5

Simple and best practice solution for 0.5x^2=3x+0.5 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=3x+0.5 equation:


Simplifying
0.5x2 = 3x + 0.5

Reorder the terms:
0.5x2 = 0.5 + 3x

Solving
0.5x2 = 0.5 + 3x

Solving for variable 'x'.

Reorder the terms:
-0.5 + -3x + 0.5x2 = 0.5 + 3x + -0.5 + -3x

Reorder the terms:
-0.5 + -3x + 0.5x2 = 0.5 + -0.5 + 3x + -3x

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + -3x + 0.5x2 = 0.0 + 3x + -3x
-0.5 + -3x + 0.5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-0.5 + -3x + 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'.
-1 + -6x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x + x2 = 0 + 1
-6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6x + x2 = 1

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 1 + 9

Reorder the terms:
9 + -6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + -6x + x2 = 10

Factor a perfect square on the left side:
(x + -3)(x + -3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -3) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + -3 = 3.16227766 Simplifying x + -3 = 3.16227766 Reorder the terms: -3 + x = 3.16227766 Solving -3 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.16227766 + 3 x = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 x = 6.16227766 Simplifying x = 6.16227766

Subproblem 2

x + -3 = -3.16227766 Simplifying x + -3 = -3.16227766 Reorder the terms: -3 + x = -3.16227766 Solving -3 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.16227766 + 3 x = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 x = -0.16227766 Simplifying x = -0.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.16227766, -0.16227766}

See similar equations:

| 64y^3-y=0 | | 2x^3+13x^2+6x=0 | | 6Y-2Y-6Y= | | 12x+5*0=11 | | 7(2x-3)=4(x+3)+15 | | 25y^3-y=0 | | 12*0+5y=11 | | 4(2x+3)=5(x-3)+10 | | 3(2x-2)=7x | | (y-5)-(y+4)=2y | | 10h=20+5h | | 3X(-5+4X)=0 | | 2y^2-162=0 | | 6x+6=5x | | c^2-50=-23c | | 4(x-6)+8=6(x+2)-10 | | 6h=10+4h | | 121m^2=16 | | 12a-2=5-9a | | 12x-73-8x=63 | | 3x^2+27x+42=0 | | P^2-2p=8 | | 4x+1=5x-8 | | -35-7z+2z^2=0 | | 5x+2=x-1 | | 7.4=y-7 | | 1.5x+2.9=0.7x-4.62 | | 12x-142-16x=78 | | 10x+2=5x-7 | | 32-68z+8z^2=0 | | 8x+2x-365=175 | | 5t+10s+10=520 |

Equations solver categories