2x(2x+1)=5

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


Simplifying
2x(2x + 1) = 5

Reorder the terms:
2x(1 + 2x) = 5
(1 * 2x + 2x * 2x) = 5
(2x + 4x2) = 5

Solving
2x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 2x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 2x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.5x + x2 = 0 + 1.25
0.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.5x + x2 = 1.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.25 + 0.0625

Combine like terms: 1.25 + 0.0625 = 1.3125
0.0625 + 0.5x + x2 = 1.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.145643924 and -1.145643924.

Subproblem 1

x + 0.25 = 1.145643924 Simplifying x + 0.25 = 1.145643924 Reorder the terms: 0.25 + x = 1.145643924 Solving 0.25 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.145643924 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.145643924 + -0.25 x = 1.145643924 + -0.25 Combine like terms: 1.145643924 + -0.25 = 0.895643924 x = 0.895643924 Simplifying x = 0.895643924

Subproblem 2

x + 0.25 = -1.145643924 Simplifying x + 0.25 = -1.145643924 Reorder the terms: 0.25 + x = -1.145643924 Solving 0.25 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.145643924 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.145643924 + -0.25 x = -1.145643924 + -0.25 Combine like terms: -1.145643924 + -0.25 = -1.395643924 x = -1.395643924 Simplifying x = -1.395643924

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.895643924, -1.395643924}

See similar equations:

| 15-24x+11x= | | 14+8n=4n+6n | | 6(1+3x)=-120 | | 4x^2+12x=7 | | 6k-8+6=-2+k | | 3(3.3-1)=9 | | 37(x-148)=74 | | 15x+21=36-36x+24 | | 0=x^2+x-e^4 | | 4(7-6x)=-116 | | 8k=10k+12 | | -72+X^2+-1x=0 | | 7/x-6-3/4x-24 | | y=5x^2-10x+37 | | 8x^2+16x^9-28x^4+20= | | 8(3-n)=88 | | 245=5(6k+7) | | 4/x+28 | | -x^2-9x-2=0 | | 88=-2n+7(4n-6) | | y=x^2+16x+17 | | -8(4v-5)=296 | | p=23 | | 5-(-2+27)= | | 4(-7+4b)=-108 | | -3y+2x=-5x+5 | | 15=z-342 | | 2=r/12+3 | | 4n-6=n+9 | | -8(a+4)=-88 | | 11=7+x/2 | | 3(2n+7)-4n+6=8n+3 |

Equations solver categories