12x^2-84x+1=0

Simple and best practice solution for 12x^2-84x+1=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 12x^2-84x+1=0 equation:


Simplifying
12x2 + -84x + 1 = 0

Reorder the terms:
1 + -84x + 12x2 = 0

Solving
1 + -84x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
0.08333333333 + -7x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + -7x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + -7x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + -7x + x2 = 0 + -0.08333333333
-7x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
-7x + x2 = -0.08333333333

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -0.08333333333 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -0.08333333333 + 12.25

Combine like terms: -0.08333333333 + 12.25 = 12.16666666667
12.25 + -7x + x2 = 12.16666666667

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 12.16666666667

Calculate the square root of the right side: 3.488074923

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.488074923 and -3.488074923.

Subproblem 1

x + -3.5 = 3.488074923 Simplifying x + -3.5 = 3.488074923 Reorder the terms: -3.5 + x = 3.488074923 Solving -3.5 + x = 3.488074923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.488074923 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.488074923 + 3.5 x = 3.488074923 + 3.5 Combine like terms: 3.488074923 + 3.5 = 6.988074923 x = 6.988074923 Simplifying x = 6.988074923

Subproblem 2

x + -3.5 = -3.488074923 Simplifying x + -3.5 = -3.488074923 Reorder the terms: -3.5 + x = -3.488074923 Solving -3.5 + x = -3.488074923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.488074923 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.488074923 + 3.5 x = -3.488074923 + 3.5 Combine like terms: -3.488074923 + 3.5 = 0.011925077 x = 0.011925077 Simplifying x = 0.011925077

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.988074923, 0.011925077}

See similar equations:

| g=5a^2-8 | | 9+n=-84 | | 4(5z-1)-2(z+8)=5(z+1) | | -7x+72=5x | | g(a^2)=5(a^2)-8(a^2) | | -9k-10=-118 | | -9k-10=-188 | | f(-6)=-60+3(36) | | x/6-7=-8 | | -59=-3-4v | | 4+8(x-5)=7-4(x-1) | | 2lnt(x+2)=4 | | -5x^3+25x^2-30x=0 | | -5(5n+1)=4 | | f(-6)=10x+3x^2 | | 30=a+20 | | 2In(x+2)=4 | | h(x)=2x^2+4x+11 | | y+3y+120=180 | | y+3x+120=180 | | -5=9(2-2y)+13 | | 5t+5=30 | | z^3=-j | | 5p-21=24 | | 2x+2xy+2y= | | In(3x)+in(2x)=9 | | x*2+1=5 | | 2(4x-1)=99-7(3-4x) | | -6(-1x+5)=-12 | | 3(6+7x)=18 | | -4(2x-2)=48 | | P-10=5(2w-4) |

Equations solver categories