2x^2+1=5x

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


Simplifying
2x2 + 1 = 5x

Reorder the terms:
1 + 2x2 = 5x

Solving
1 + 2x2 = 5x

Solving for variable 'x'.

Reorder the terms:
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 = 1.0625
1.5625 + -2.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + -1.25 = 1.030776406 Simplifying x + -1.25 = 1.030776406 Reorder the terms: -1.25 + x = 1.030776406 Solving -1.25 + x = 1.030776406 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 = 1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.030776406 + 1.25 x = 1.030776406 + 1.25 Combine like terms: 1.030776406 + 1.25 = 2.280776406 x = 2.280776406 Simplifying x = 2.280776406

Subproblem 2

x + -1.25 = -1.030776406 Simplifying x + -1.25 = -1.030776406 Reorder the terms: -1.25 + x = -1.030776406 Solving -1.25 + x = -1.030776406 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 = -1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.030776406 + 1.25 x = -1.030776406 + 1.25 Combine like terms: -1.030776406 + 1.25 = 0.219223594 x = 0.219223594 Simplifying x = 0.219223594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.280776406, 0.219223594}

See similar equations:

| 5x-4(4x-7)=-10 | | -2x+3y=4 | | 7x+4(x+3)=20 | | -2(x+5)-2=23 | | -5(3x+4)-19=12 | | 25x^2-30x+9=81 | | x^2-22x+121=225 | | 4x-1=3x+6 | | x^2-10x+25=144 | | 5x-16=54 | | 3x-4=10x-1 | | 3x-4=10-1 | | 6(9x+2)=6 | | 11x-3=-7x | | 11x-3=-7 | | 4x+21-10x=3-5x-15 | | 8X(6X+8X)=7(9+7) | | 5(x+6)=3x+12 | | 3(x+9)=30 | | 2(x-22)+4(x-4)=48 | | C=8.5x+6y | | 4(x-3)+19=3(x+5) | | 4(x+8)=28 | | 9x+5-27x=7-8x-15 | | 12x-(6x-2)=38 | | 18=8+10(x-11) | | 7x-2(x-3y)-4y= | | X=2.5X+10 | | 9x+1.4=4x+0.9 | | 5x+1.5=2x+0.6 | | 4x+1.5=x | | 3x-0.1=2x |

Equations solver categories