x^2-30.8x+78.4=0

Simple and best practice solution for x^2-30.8x+78.4=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^2-30.8x+78.4=0 equation:


Simplifying
x2 + -30.8x + 78.4 = 0

Reorder the terms:
78.4 + -30.8x + x2 = 0

Solving
78.4 + -30.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-78.4' to each side of the equation.
78.4 + -30.8x + -78.4 + x2 = 0 + -78.4

Reorder the terms:
78.4 + -78.4 + -30.8x + x2 = 0 + -78.4

Combine like terms: 78.4 + -78.4 = 0.0
0.0 + -30.8x + x2 = 0 + -78.4
-30.8x + x2 = 0 + -78.4

Combine like terms: 0 + -78.4 = -78.4
-30.8x + x2 = -78.4

The x term is -30.8x.  Take half its coefficient (-15.4).
Square it (237.16) and add it to both sides.

Add '237.16' to each side of the equation.
-30.8x + 237.16 + x2 = -78.4 + 237.16

Reorder the terms:
237.16 + -30.8x + x2 = -78.4 + 237.16

Combine like terms: -78.4 + 237.16 = 158.76
237.16 + -30.8x + x2 = 158.76

Factor a perfect square on the left side:
(x + -15.4)(x + -15.4) = 158.76

Calculate the square root of the right side: 12.6

Break this problem into two subproblems by setting 
(x + -15.4) equal to 12.6 and -12.6.

Subproblem 1

x + -15.4 = 12.6 Simplifying x + -15.4 = 12.6 Reorder the terms: -15.4 + x = 12.6 Solving -15.4 + x = 12.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.4' to each side of the equation. -15.4 + 15.4 + x = 12.6 + 15.4 Combine like terms: -15.4 + 15.4 = 0.0 0.0 + x = 12.6 + 15.4 x = 12.6 + 15.4 Combine like terms: 12.6 + 15.4 = 28 x = 28 Simplifying x = 28

Subproblem 2

x + -15.4 = -12.6 Simplifying x + -15.4 = -12.6 Reorder the terms: -15.4 + x = -12.6 Solving -15.4 + x = -12.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.4' to each side of the equation. -15.4 + 15.4 + x = -12.6 + 15.4 Combine like terms: -15.4 + 15.4 = 0.0 0.0 + x = -12.6 + 15.4 x = -12.6 + 15.4 Combine like terms: -12.6 + 15.4 = 2.8 x = 2.8 Simplifying x = 2.8

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28, 2.8}

See similar equations:

| 0.3x+62.5=298 | | 32x^2=50 | | 4t^4-64=0 | | 0.8x+13.2=188 | | 0.07(3t+5)=0.21(t-2+0.077) | | 2x^3-x^2-18x-9=0 | | 0.6x+12.2=235 | | u+426=665 | | -7-(-7)=-7+(7) | | 3(g-18)=105 | | 7x+8=(7x+9) | | 16t^2+128t=192 | | -2(x-3)=-(x+5) | | -7x^2-28x=-224 | | 32+0.2c=y | | 8(g-10)=120 | | 9x^2+45x-54=0 | | -2(c-3)=-(x+5) | | 14(v+3)-2v=4(3v+2)-10 | | r^2+17r+60=r-4 | | 4x^2=6x-1 | | s^2-12s=0 | | 25t^2+36=60t | | 2(g-15)=120 | | 25r^2+64=80r | | 3y-2(y+3)=0 | | 2b-3+b-4= | | 4a-6+9a-5= | | (x+3)(3x-1)=10x-2x^2 | | 3n-9-n= | | 1-7a-7-8a= | | r-6-2= |

Equations solver categories