.5x^2+2x=3x+7

Simple and best practice solution for .5x^2+2x=3x+7 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 .5x^2+2x=3x+7 equation:


Simplifying
0.5x2 + 2x = 3x + 7

Reorder the terms:
2x + 0.5x2 = 3x + 7

Reorder the terms:
2x + 0.5x2 = 7 + 3x

Solving
2x + 0.5x2 = 7 + 3x

Solving for variable 'x'.

Reorder the terms:
-7 + 2x + -3x + 0.5x2 = 7 + 3x + -7 + -3x

Combine like terms: 2x + -3x = -1x
-7 + -1x + 0.5x2 = 7 + 3x + -7 + -3x

Reorder the terms:
-7 + -1x + 0.5x2 = 7 + -7 + 3x + -3x

Combine like terms: 7 + -7 = 0
-7 + -1x + 0.5x2 = 0 + 3x + -3x
-7 + -1x + 0.5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-7 + -1x + 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'.
-14 + -2x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -2x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -2x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -2x + x2 = 0 + 14
-2x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-2x + x2 = 14

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 = 14 + 1

Reorder the terms:
1 + -2x + x2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + -2x + x2 = 15

Factor a perfect square on the left side:
(x + -1)(x + -1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -1) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + -1 = 3.872983346 Simplifying x + -1 = 3.872983346 Reorder the terms: -1 + x = 3.872983346 Solving -1 + x = 3.872983346 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 = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.872983346 + 1 x = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 x = 4.872983346 Simplifying x = 4.872983346

Subproblem 2

x + -1 = -3.872983346 Simplifying x + -1 = -3.872983346 Reorder the terms: -1 + x = -3.872983346 Solving -1 + x = -3.872983346 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 = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.872983346 + 1 x = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 x = -2.872983346 Simplifying x = -2.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.872983346, -2.872983346}

See similar equations:

| a/6x=5x | | 24/14=m/35 | | 41=-7x+2(-4-32) | | -0.2x(x-6)+x=0.3(4-x) | | -5n+6n+15n-3n=3 | | 50+10t=30 | | -3x(2x+9)=0 | | 4m/3-m/6=-3 | | -45=63+9n | | 99-4x=14x+15 | | F(x)=4(6) | | 7-10x=157-45x | | 6t-54=36 | | r/3+7-r/5=3 | | 5/6(6x-3) | | -12m-24= | | 0.75+2x-1=3x-0.4 | | 7x-6(-x+20)=-224 | | -6y+9=-6y+6 | | F(6)=4x | | (-4.8y+20.1)-(12.7y+9.3)= | | 5p+5=14+4p | | -x+7x-7+2=29+2x+2 | | 55=-138+x | | 10b+15+6b=39 | | 4*2/10 | | (3x+4)(x+5)=0 | | 5x+31=13x-37 | | 94=88+d | | 21=3x-7(-2x+14) | | 299=-290+b | | 1/2(2x-5)=4 |

Equations solver categories