2x^2=5x+1

Simple and best practice solution for 2x^2=5x+1 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 2x^2=5x+1 equation:


Simplifying
2x2 = 5x + 1

Reorder the terms:
2x2 = 1 + 5x

Solving
2x2 = 1 + 5x

Solving for variable 'x'.

Reorder the terms:
-1 + -5x + 2x2 = 1 + 5x + -1 + -5x

Reorder the terms:
-1 + -5x + 2x2 = 1 + -1 + 5x + -5x

Combine like terms: 1 + -1 = 0
-1 + -5x + 2x2 = 0 + 5x + -5x
-1 + -5x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-1 + -5x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2.5x + x2 = 0 + 0.5
-2.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2.5x + x2 = 0.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 0.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 0.5 + 1.5625

Combine like terms: 0.5 + 1.5625 = 2.0625
1.5625 + -2.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.436140662 and -1.436140662.

Subproblem 1

x + -1.25 = 1.436140662 Simplifying x + -1.25 = 1.436140662 Reorder the terms: -1.25 + x = 1.436140662 Solving -1.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.436140662 + 1.25 x = 1.436140662 + 1.25 Combine like terms: 1.436140662 + 1.25 = 2.686140662 x = 2.686140662 Simplifying x = 2.686140662

Subproblem 2

x + -1.25 = -1.436140662 Simplifying x + -1.25 = -1.436140662 Reorder the terms: -1.25 + x = -1.436140662 Solving -1.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.436140662 + 1.25 x = -1.436140662 + 1.25 Combine like terms: -1.436140662 + 1.25 = -0.186140662 x = -0.186140662 Simplifying x = -0.186140662

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.686140662, -0.186140662}

See similar equations:

| -4(10-9-6)= | | 6-2[x-5(x+3)]=20 | | 4(13-5)= | | 50-[2+5y-3(Y+4)]=-2(3y-7)-[9(y-1)-7y+11] | | 0.085=1.7m | | -2.4(5h-10+4)= | | 2ydx-8(x+6)dy=0 | | 2-3(1-y)=2(y+1) | | 11-2(x+1)=x | | 1.5(6c+10d+3)= | | -156=-4c | | 5x+3=-5+8(1+5x) | | 8y-10=10y-30 | | -3(-12-3d-8)= | | 4n=-60 | | 11p=88 | | (x+3)(x-2)=0.01 | | 144=-2y | | -11-6x=-8-3(1+2x) | | -1=5(x-3)-(x-6) | | 7(2x+7+9y)= | | 4(2y-9)-(5y+6)=0 | | 8(p-6-5)= | | -3(5-2c)-(4c+7)=0 | | 6k=138 | | 4(-2x-3)+6x=18 | | 10x+6=-4(x+1) | | 3(1-2a)-(6-2a)=-7 | | 2(3x+1)-5x=-6 | | 3(x+4+9)= | | 28-c=57 | | -(12-3z)=6(z+2) |

Equations solver categories