0.5=-0.5x^2+x+24

Simple and best practice solution for 0.5=-0.5x^2+x+24 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 0.5=-0.5x^2+x+24 equation:


Simplifying
0.5 = -0.5x2 + x + 24

Reorder the terms:
0.5 = 24 + x + -0.5x2

Solving
0.5 = 24 + x + -0.5x2

Solving for variable 'x'.

Combine like terms: 0.5 + -24 = -23.5
-23.5 + -1x + 0.5x2 = 24 + x + -0.5x2 + -24 + -1x + 0.5x2

Reorder the terms:
-23.5 + -1x + 0.5x2 = 24 + -24 + x + -1x + -0.5x2 + 0.5x2

Combine like terms: 24 + -24 = 0
-23.5 + -1x + 0.5x2 = 0 + x + -1x + -0.5x2 + 0.5x2
-23.5 + -1x + 0.5x2 = x + -1x + -0.5x2 + 0.5x2

Combine like terms: x + -1x = 0
-23.5 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2
-23.5 + -1x + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
-23.5 + -1x + 0.5x2 = 0.0

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

Divide each side by '0.5'.
-47 + -2x + x2 = 0

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -2x + 47 + x2 = 0 + 47

Reorder the terms:
-47 + 47 + -2x + x2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -2x + x2 = 0 + 47
-2x + x2 = 0 + 47

Combine like terms: 0 + 47 = 47
-2x + x2 = 47

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 47 + 1

Reorder the terms:
1 + -2x + x2 = 47 + 1

Combine like terms: 47 + 1 = 48
1 + -2x + x2 = 48

Factor a perfect square on the left side:
(x + -1)(x + -1) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + -1) equal to 6.92820323 and -6.92820323.

Subproblem 1

x + -1 = 6.92820323 Simplifying x + -1 = 6.92820323 Reorder the terms: -1 + x = 6.92820323 Solving -1 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.92820323 + 1 x = 6.92820323 + 1 Combine like terms: 6.92820323 + 1 = 7.92820323 x = 7.92820323 Simplifying x = 7.92820323

Subproblem 2

x + -1 = -6.92820323 Simplifying x + -1 = -6.92820323 Reorder the terms: -1 + x = -6.92820323 Solving -1 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.92820323 + 1 x = -6.92820323 + 1 Combine like terms: -6.92820323 + 1 = -5.92820323 x = -5.92820323 Simplifying x = -5.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.92820323, -5.92820323}

See similar equations:

| -6x^2+18=7+2x | | X^4-3x^3+1=0 | | p+19=44 | | -4=c/2+3 | | 3y+3x=3y-23 | | x^2+12-16=0 | | 0.5=-0.5x^2+0.5x+15 | | 5x+5x-4x+3= | | 1+g=-7 | | 2x^2-21x-40=0 | | -7n^2+4n-23=-10n^2-8 | | -1x+2y+4=0 | | 2x+12=-18 | | 6=e/4+2 | | 6=e/4+4 | | 6f+20=-2f-4 | | 44=4n | | 5(2x+6)= | | .60x-2=3.333 | | 0.5(-6)-8= | | 3+(5+2-4)2+12= | | 11+(-9)2= | | -8b^2+4b=-8 | | h=1/2(h+h) | | 3/4b=15 | | (-2)+-63+3= | | 3/4b+15 | | (-2)+-6+3= | | 6v^2-3=0 | | x+(x^1/2)=20 | | 1/2=4(5x-3) | | 3(-2)+-6+3= |

Equations solver categories