5x^2+5x=1

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


Simplifying
5x2 + 5x = 1

Reorder the terms:
5x + 5x2 = 1

Solving
5x + 5x2 = 1

Solving for variable 'x'.

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

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

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

Divide each side by '5'.
-0.2 + x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x + x2 = 0 + 0.2
x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
x + x2 = 0.2

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.
 + 0.25 + x2 = 0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
1.25 + x2 = 0.45

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1

x + 0.5 = 0.670820393 Simplifying x + 0.5 = 0.670820393 Reorder the terms: 0.5 + x = 0.670820393 Solving 0.5 + x = 0.670820393 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 = 0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.670820393 + -0.5 x = 0.670820393 + -0.5 Combine like terms: 0.670820393 + -0.5 = 0.170820393 x = 0.170820393 Simplifying x = 0.170820393

Subproblem 2

x + 0.5 = -0.670820393 Simplifying x + 0.5 = -0.670820393 Reorder the terms: 0.5 + x = -0.670820393 Solving 0.5 + x = -0.670820393 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 = -0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.670820393 + -0.5 x = -0.670820393 + -0.5 Combine like terms: -0.670820393 + -0.5 = -1.170820393 x = -1.170820393 Simplifying x = -1.170820393

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.170820393, -1.170820393}

See similar equations:

| -10=5-8/-6 | | 1/8=x/53 | | x/10=9/45 | | x/4+x/5=9 | | 20/50=18/x | | 10v^2=13+3 | | 1/2=(t-3)/9 | | 10v^2=13r+3 | | 28y^7+4y^2=0 | | y/2+y/5=4/3 | | -4y-9(9y+6)=-1-5(7-y) | | 28=7-2/3t | | x/4+x/5= | | 6k^2-7k=20 | | -4x+1=-x-23 | | -6y+3(6y+4)=-7+9(8-y) | | 10y-12=30+6y | | 7x+5-3(x+1)=9x+6 | | 3/4t=3/5 | | 615+25x=975-15x | | 4x+9=-3x | | 8+c/4=12 | | 2+2=85 | | j^2-3j=0 | | 10X^2-23x-12=0 | | -1=-6x+7x-7 | | (1/9)x^2+(1/3)+(1/4)=0 | | -3z-1+8x-3=6x+7-5x | | 305689000.00-15000000.00x=300000000 | | 4x+16=-24 | | 2x+34=9x | | -(1/2+7/2i)+(7/3+11/3i) |

Equations solver categories