1077=27x^2+40x

Simple and best practice solution for 1077=27x^2+40x 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 1077=27x^2+40x equation:


Simplifying
1077 = 27x2 + 40x

Reorder the terms:
1077 = 40x + 27x2

Solving
1077 = 40x + 27x2

Solving for variable 'x'.

Reorder the terms:
1077 + -40x + -27x2 = 40x + -40x + 27x2 + -27x2

Combine like terms: 40x + -40x = 0
1077 + -40x + -27x2 = 0 + 27x2 + -27x2
1077 + -40x + -27x2 = 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
1077 + -40x + -27x2 = 0

Begin completing the square.  Divide all terms by
-27 the coefficient of the squared term: 

Divide each side by '-27'.
-39.88888889 + 1.481481481x + x2 = 0

Move the constant term to the right:

Add '39.88888889' to each side of the equation.
-39.88888889 + 1.481481481x + 39.88888889 + x2 = 0 + 39.88888889

Reorder the terms:
-39.88888889 + 39.88888889 + 1.481481481x + x2 = 0 + 39.88888889

Combine like terms: -39.88888889 + 39.88888889 = 0.00000000
0.00000000 + 1.481481481x + x2 = 0 + 39.88888889
1.481481481x + x2 = 0 + 39.88888889

Combine like terms: 0 + 39.88888889 = 39.88888889
1.481481481x + x2 = 39.88888889

The x term is 1.481481481x.  Take half its coefficient (0.7407407405).
Square it (0.5486968446) and add it to both sides.

Add '0.5486968446' to each side of the equation.
1.481481481x + 0.5486968446 + x2 = 39.88888889 + 0.5486968446

Reorder the terms:
0.5486968446 + 1.481481481x + x2 = 39.88888889 + 0.5486968446

Combine like terms: 39.88888889 + 0.5486968446 = 40.4375857346
0.5486968446 + 1.481481481x + x2 = 40.4375857346

Factor a perfect square on the left side:
(x + 0.7407407405)(x + 0.7407407405) = 40.4375857346

Calculate the square root of the right side: 6.359055412

Break this problem into two subproblems by setting 
(x + 0.7407407405) equal to 6.359055412 and -6.359055412.

Subproblem 1

x + 0.7407407405 = 6.359055412 Simplifying x + 0.7407407405 = 6.359055412 Reorder the terms: 0.7407407405 + x = 6.359055412 Solving 0.7407407405 + x = 6.359055412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7407407405' to each side of the equation. 0.7407407405 + -0.7407407405 + x = 6.359055412 + -0.7407407405 Combine like terms: 0.7407407405 + -0.7407407405 = 0.0000000000 0.0000000000 + x = 6.359055412 + -0.7407407405 x = 6.359055412 + -0.7407407405 Combine like terms: 6.359055412 + -0.7407407405 = 5.6183146715 x = 5.6183146715 Simplifying x = 5.6183146715

Subproblem 2

x + 0.7407407405 = -6.359055412 Simplifying x + 0.7407407405 = -6.359055412 Reorder the terms: 0.7407407405 + x = -6.359055412 Solving 0.7407407405 + x = -6.359055412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7407407405' to each side of the equation. 0.7407407405 + -0.7407407405 + x = -6.359055412 + -0.7407407405 Combine like terms: 0.7407407405 + -0.7407407405 = 0.0000000000 0.0000000000 + x = -6.359055412 + -0.7407407405 x = -6.359055412 + -0.7407407405 Combine like terms: -6.359055412 + -0.7407407405 = -7.0997961525 x = -7.0997961525 Simplifying x = -7.0997961525

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.6183146715, -7.0997961525}

See similar equations:

| -2(-3b+5)= | | L=78-w-3 | | 20x+500=16x+800 | | 3(x+2)+5=24 | | 2(3b-5)= | | 4+11x+1+12x=2(-7-5x)+10(5x-10) | | M-9=3(m+4)-20 | | (2v-bu)(4v-bu)=0 | | 78=l+(w+3) | | 20x+444=504 | | 10-4j=2j | | 10x-15=36 | | 18=a-1.5(4) | | 4g-9=7 | | 4x+28=4x+26 | | .02P+.06(1300-P)=65 | | 4t=2(t-7)-4 | | -5(3b+9)-15= | | 4X-3=18-3c | | 4x=16x-12 | | X+-8=-10 | | 1600-400x=0 | | -[10z-(15z+9)]=9+(4z+7) | | 6x+(6x-9)+(3x+6x)=180 | | 157=3-34 | | .5x+1=.75 | | (2u-5xa)(u-xa)=0 | | 32x=24x+120 | | 5x-4+3x+1=8x+2 | | 7(2x-3)+8x= | | -15p-5(4-4p)=2(p-5)-10 | | 20l+2m=480 |

Equations solver categories