2.431x^2-4.512x-6.719=0

Simple and best practice solution for 2.431x^2-4.512x-6.719=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 2.431x^2-4.512x-6.719=0 equation:


Simplifying
2.431x2 + -4.512x + -6.719 = 0

Reorder the terms:
-6.719 + -4.512x + 2.431x2 = 0

Solving
-6.719 + -4.512x + 2.431x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.431'.
-2.763883176 + -1.856026327x + x2 = 0

Move the constant term to the right:

Add '2.763883176' to each side of the equation.
-2.763883176 + -1.856026327x + 2.763883176 + x2 = 0 + 2.763883176

Reorder the terms:
-2.763883176 + 2.763883176 + -1.856026327x + x2 = 0 + 2.763883176

Combine like terms: -2.763883176 + 2.763883176 = 0.000000000
0.000000000 + -1.856026327x + x2 = 0 + 2.763883176
-1.856026327x + x2 = 0 + 2.763883176

Combine like terms: 0 + 2.763883176 = 2.763883176
-1.856026327x + x2 = 2.763883176

The x term is -1.856026327x.  Take half its coefficient (-0.9280131635).
Square it (0.8612084316) and add it to both sides.

Add '0.8612084316' to each side of the equation.
-1.856026327x + 0.8612084316 + x2 = 2.763883176 + 0.8612084316

Reorder the terms:
0.8612084316 + -1.856026327x + x2 = 2.763883176 + 0.8612084316

Combine like terms: 2.763883176 + 0.8612084316 = 3.6250916076
0.8612084316 + -1.856026327x + x2 = 3.6250916076

Factor a perfect square on the left side:
(x + -0.9280131635)(x + -0.9280131635) = 3.6250916076

Calculate the square root of the right side: 1.903967334

Break this problem into two subproblems by setting 
(x + -0.9280131635) equal to 1.903967334 and -1.903967334.

Subproblem 1

x + -0.9280131635 = 1.903967334 Simplifying x + -0.9280131635 = 1.903967334 Reorder the terms: -0.9280131635 + x = 1.903967334 Solving -0.9280131635 + x = 1.903967334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9280131635' to each side of the equation. -0.9280131635 + 0.9280131635 + x = 1.903967334 + 0.9280131635 Combine like terms: -0.9280131635 + 0.9280131635 = 0.0000000000 0.0000000000 + x = 1.903967334 + 0.9280131635 x = 1.903967334 + 0.9280131635 Combine like terms: 1.903967334 + 0.9280131635 = 2.8319804975 x = 2.8319804975 Simplifying x = 2.8319804975

Subproblem 2

x + -0.9280131635 = -1.903967334 Simplifying x + -0.9280131635 = -1.903967334 Reorder the terms: -0.9280131635 + x = -1.903967334 Solving -0.9280131635 + x = -1.903967334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9280131635' to each side of the equation. -0.9280131635 + 0.9280131635 + x = -1.903967334 + 0.9280131635 Combine like terms: -0.9280131635 + 0.9280131635 = 0.0000000000 0.0000000000 + x = -1.903967334 + 0.9280131635 x = -1.903967334 + 0.9280131635 Combine like terms: -1.903967334 + 0.9280131635 = -0.9759541705 x = -0.9759541705 Simplifying x = -0.9759541705

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.8319804975, -0.9759541705}

See similar equations:

| -6X-3=X+7 | | -5(x+6)=15 | | -x^2-6x-18=0 | | -3+11=13x-5-12x | | 6x-5=2x-8 | | 14+2(5)= | | 3(3x+1)+4(x-3)= | | =50-5P | | 14+2(5)=5(5)-1 | | =50P | | 4x=-124 | | 3y^3-3y^2-6y=0 | | -6(20y)= | | .21-.14x=-.28x-.34 | | 1-8t=-9-3t | | 42m=-966 | | 6y-4(y-2)+4= | | p(5)=2(5)2-6(5)+4 | | -1+b=-1 | | n+6=2 | | x+0.07x=68.48 | | k+3=0 | | x+0.07=68.48 | | 7n=-2n-36 | | 10x-45=5x+5 | | a-8=-12 | | 14+k=25 | | -9+w=-15 | | 0.06(x)+0.15(10)=0.12(x+10) | | r+6=-1 | | 3+4x=109 | | 2(6-9w)=8(4w+1) |

Equations solver categories