0.5x^2+0.5x=45

Simple and best practice solution for 0.5x^2+0.5x=45 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+0.5x=45 equation:


Simplifying
0.5x2 + 0.5x = 45

Reorder the terms:
0.5x + 0.5x2 = 45

Solving
0.5x + 0.5x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + 0.5x + 0.5x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 0.5x + 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'.
-90 + x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + x + x2 = 0 + 90
x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
x + x2 = 90

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.
 + 0.25 + x2 = 90 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 90 + 0.25

Combine like terms: 90 + 0.25 = 90.25
1.25 + x2 = 90.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 90.25

Calculate the square root of the right side: 9.5

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.5 and -9.5.

Subproblem 1

x + 0.5 = 9.5 Simplifying x + 0.5 = 9.5 Reorder the terms: 0.5 + x = 9.5 Solving 0.5 + x = 9.5 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 = 9.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.5 + -0.5 x = 9.5 + -0.5 Combine like terms: 9.5 + -0.5 = 9 x = 9 Simplifying x = 9

Subproblem 2

x + 0.5 = -9.5 Simplifying x + 0.5 = -9.5 Reorder the terms: 0.5 + x = -9.5 Solving 0.5 + x = -9.5 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 = -9.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.5 + -0.5 x = -9.5 + -0.5 Combine like terms: -9.5 + -0.5 = -10 x = -10 Simplifying x = -10

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9, -10}

See similar equations:

| 96=3x^2+2 | | a+bx^2=0 | | 3/7(7b-1)=(b-5) | | 4+3(2z-5)=2(3z-4) | | X=.43(-1)+6.43 | | 0.4x-12=0.4 | | 7(6x-3)=18.5-5x | | 0.4c=1.75 | | 0.4=1.75 | | 2x=12y+6 | | 5x+50=15x | | 5k-35-7+k= | | 0.8f=7 | | 8/20=x/30 | | 108=8x+x | | 96=4x+2 | | -6.3(2p+4)-1.3(4p-6)= | | 5.4s=6 | | 80x+200=70x+230 | | 4.5x-17=2.5x-5 | | -18.5=-7.5+3.5(r+2.5) | | 4(5-x)=6(5+7x) | | 1.5x-4=-6-9 | | 1+3x=(4(0.5+0.75x)-1) | | 15-y=5 | | 9/14•6/10 | | 21x+5=85 | | 10-12=12r+24 | | -6(-7x)-(1+x)=178 | | -229=-4+9(4a+7) | | 4+17r-1=7r+94-3r | | -3(4x+15)-(10+x)=35 |

Equations solver categories