x^2+78x-77=0

Simple and best practice solution for x^2+78x-77=0 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^2+78x-77=0 equation:


Simplifying
x2 + 78x + -77 = 0

Reorder the terms:
-77 + 78x + x2 = 0

Solving
-77 + 78x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '77' to each side of the equation.
-77 + 78x + 77 + x2 = 0 + 77

Reorder the terms:
-77 + 77 + 78x + x2 = 0 + 77

Combine like terms: -77 + 77 = 0
0 + 78x + x2 = 0 + 77
78x + x2 = 0 + 77

Combine like terms: 0 + 77 = 77
78x + x2 = 77

The x term is 78x.  Take half its coefficient (39).
Square it (1521) and add it to both sides.

Add '1521' to each side of the equation.
78x + 1521 + x2 = 77 + 1521

Reorder the terms:
1521 + 78x + x2 = 77 + 1521

Combine like terms: 77 + 1521 = 1598
1521 + 78x + x2 = 1598

Factor a perfect square on the left side:
(x + 39)(x + 39) = 1598

Calculate the square root of the right side: 39.974992183

Break this problem into two subproblems by setting 
(x + 39) equal to 39.974992183 and -39.974992183.

Subproblem 1

x + 39 = 39.974992183 Simplifying x + 39 = 39.974992183 Reorder the terms: 39 + x = 39.974992183 Solving 39 + x = 39.974992183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = 39.974992183 + -39 Combine like terms: 39 + -39 = 0 0 + x = 39.974992183 + -39 x = 39.974992183 + -39 Combine like terms: 39.974992183 + -39 = 0.974992183 x = 0.974992183 Simplifying x = 0.974992183

Subproblem 2

x + 39 = -39.974992183 Simplifying x + 39 = -39.974992183 Reorder the terms: 39 + x = -39.974992183 Solving 39 + x = -39.974992183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = -39.974992183 + -39 Combine like terms: 39 + -39 = 0 0 + x = -39.974992183 + -39 x = -39.974992183 + -39 Combine like terms: -39.974992183 + -39 = -78.974992183 x = -78.974992183 Simplifying x = -78.974992183

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.974992183, -78.974992183}

See similar equations:

| 29(5x+3)=26 | | z-21=-22 | | 9+4t=4 | | j+25=57 | | 20-22=80 | | 55+j=72 | | X+(x+2)+(x+4)=7 | | z+18=38 | | 5x+4=8x^2 | | 3x*2x^2=108 | | x^2-3xy+2y^2= | | 14p-6p=23-7 | | 14p+6p=-23+-7 | | 6x-36=19-5x | | x^2+46x-4=0 | | 50=-24.714x+202.62 | | x^2-7x+88=0 | | 0=a*7+b | | 0=-2.5*7+x | | 3(3w+9)=3 | | 10=3x+17.5 | | 10=3x+y | | 2-(3+x)=5x | | 9d+4=22 | | -8(2t+9)=152 | | 16x+(8x+4)=15 | | 10(s-8)=-154 | | 2(3x+1)+5x+3= | | 4x+13=-170-8x | | 10x+5-5(3x-1)= | | 8x+(5x+3)=17 | | 4(4s+6)=40 |

Equations solver categories