3x^2+x=7.5

Simple and best practice solution for 3x^2+x=7.5 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 3x^2+x=7.5 equation:


Simplifying
3x2 + x = 7.5

Reorder the terms:
x + 3x2 = 7.5

Solving
x + 3x2 = 7.5

Solving for variable 'x'.

Reorder the terms:
-7.5 + x + 3x2 = 7.5 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
-7.5 + x + 3x2 = 0.0

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

Divide each side by '3'.
-2.5 + 0.3333333333x + x2 = 0.0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.3333333333x + 2.5 + x2 = 0.0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.3333333333x + x2 = 0.0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.3333333333x + x2 = 0.0 + 2.5
0.3333333333x + x2 = 0.0 + 2.5

Combine like terms: 0.0 + 2.5 = 2.5
0.3333333333x + x2 = 2.5

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.
0.3333333333x + 0.25 + x2 = 2.5 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + 0.3333333333x + x2 = 2.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

x + 0.5 = 1.658312395 Simplifying x + 0.5 = 1.658312395 Reorder the terms: 0.5 + x = 1.658312395 Solving 0.5 + x = 1.658312395 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 = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.658312395 + -0.5 x = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 x = 1.158312395 Simplifying x = 1.158312395

Subproblem 2

x + 0.5 = -1.658312395 Simplifying x + 0.5 = -1.658312395 Reorder the terms: 0.5 + x = -1.658312395 Solving 0.5 + x = -1.658312395 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 = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.658312395 + -0.5 x = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 x = -2.158312395 Simplifying x = -2.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.158312395, -2.158312395}

See similar equations:

| tn=3n+6 | | 3x+1=1(3x+1) | | (-4x^2+3)+(-5x^2+1)= | | (-3x^2+9x)+(8x^2+5x)= | | 24=5x-9x | | Y+5=-9x+0 | | 4x^5-44x^4+121x^3=0 | | 24x-5=10x-53 | | -3w+35=4(w-7) | | (7x+5)-(x^2+x)= | | Tn=5n+4 | | 22x^5-44x^4+121x^3=0 | | 0.55x+0.45(2-x)=0.5(-1) | | 37x^57= | | y=x^2/10-3*x | | (3x-1)+(-7x-8)= | | -x=-12/7-4/7y | | (6x^2+9x-1)-(-2x+6)= | | x^3-24x-24=0 | | x^3-48=0 | | -150/-15= | | f(x)=log^2(5-x) | | 5+y=-2x+0 | | 4n=7 | | -3x-5(5x+8)=-180 | | -6:2/7 | | 5x+12=4x-13 | | -6=2/7x | | 1/49=7^(1-x) | | x+(x+2)+4x+20=742 | | Log^5(5x-30)=3 | | 2x+u=12 |

Equations solver categories