x(2x+1)=42

Simple and best practice solution for x(2x+1)=42 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 x(2x+1)=42 equation:


Simplifying
x(2x + 1) = 42

Reorder the terms:
x(1 + 2x) = 42
(1 * x + 2x * x) = 42
(1x + 2x2) = 42

Solving
1x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 1x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 1x + 2x2 = 0

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

Divide each side by '2'.
-21 + 0.5x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 0.5x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 0.5x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 0.5x + x2 = 0 + 21
0.5x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
0.5x + x2 = 21

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 = 21 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 21 + 0.0625

Combine like terms: 21 + 0.0625 = 21.0625
0.0625 + 0.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + 0.25) equal to 4.589389938 and -4.589389938.

Subproblem 1

x + 0.25 = 4.589389938 Simplifying x + 0.25 = 4.589389938 Reorder the terms: 0.25 + x = 4.589389938 Solving 0.25 + x = 4.589389938 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 = 4.589389938 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.589389938 + -0.25 x = 4.589389938 + -0.25 Combine like terms: 4.589389938 + -0.25 = 4.339389938 x = 4.339389938 Simplifying x = 4.339389938

Subproblem 2

x + 0.25 = -4.589389938 Simplifying x + 0.25 = -4.589389938 Reorder the terms: 0.25 + x = -4.589389938 Solving 0.25 + x = -4.589389938 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 = -4.589389938 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.589389938 + -0.25 x = -4.589389938 + -0.25 Combine like terms: -4.589389938 + -0.25 = -4.839389938 x = -4.839389938 Simplifying x = -4.839389938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.339389938, -4.839389938}

See similar equations:

| 2.3x+0.6x=3.1 | | 3=3(2)-2 | | 2.3x+0.6x=3.1x | | 4(x+-8)+7=-5(x-8)-29 | | ln(2x-9)=4 | | 18=-6x-30x | | -2u-34=6(u+5) | | 0.24=In(y) | | 4x+2x+6=36 | | -9(v-6)=-3v+48 | | 25x+5x=30 | | 8y-30=2(y+3) | | 16t^2+30t+78=0 | | 2(x+2)(x-8)=0 | | log5(1/5) | | 8(x-2)-5x=-34 | | (x-2)(-1x-1)=0 | | 64h^2+27=0 | | (8x+5)(3x+1)-12=4 | | 7d+15-3d=27 | | 7x=8+14x | | 2x-17=90 | | 2-3i/1-2i | | -8(2x+1)=0 | | 2x^2-(x/4)=0 | | -2=-8-10 | | -2-9(-8)=90 | | -3x^3+4x^2-3x+2=0 | | y^1=-2x+3y-5 | | -x-9y=90 | | 300x-2=43y | | 49-h^2-2ph+4p^2=0 |

Equations solver categories