10x^2-11x-14=0

Simple and best practice solution for 10x^2-11x-14=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 10x^2-11x-14=0 equation:


Simplifying
10x2 + -11x + -14 = 0

Reorder the terms:
-14 + -11x + 10x2 = 0

Solving
-14 + -11x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-1.4 + -1.1x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + -1.1x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + -1.1x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + -1.1x + x2 = 0 + 1.4
-1.1x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
-1.1x + x2 = 1.4

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = 1.4 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = 1.4 + 0.3025

Combine like terms: 1.4 + 0.3025 = 1.7025
0.3025 + -1.1x + x2 = 1.7025

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 1.7025

Calculate the square root of the right side: 1.304798835

Break this problem into two subproblems by setting 
(x + -0.55) equal to 1.304798835 and -1.304798835.

Subproblem 1

x + -0.55 = 1.304798835 Simplifying x + -0.55 = 1.304798835 Reorder the terms: -0.55 + x = 1.304798835 Solving -0.55 + x = 1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 1.304798835 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.304798835 + 0.55 x = 1.304798835 + 0.55 Combine like terms: 1.304798835 + 0.55 = 1.854798835 x = 1.854798835 Simplifying x = 1.854798835

Subproblem 2

x + -0.55 = -1.304798835 Simplifying x + -0.55 = -1.304798835 Reorder the terms: -0.55 + x = -1.304798835 Solving -0.55 + x = -1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -1.304798835 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.304798835 + 0.55 x = -1.304798835 + 0.55 Combine like terms: -1.304798835 + 0.55 = -0.754798835 x = -0.754798835 Simplifying x = -0.754798835

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.854798835, -0.754798835}

See similar equations:

| 321+3x=345+5x | | 8+4(2x-2)=16+4x | | -2x^2-7+4=0 | | 20x+2x=45+7x | | a/4=4=16 | | (18+2x)(30+2x)=1900 | | 2/3-10=14 | | 11x+17y=-3 | | 21x^3y^2+7xy= | | 8w+6y= | | 2log(4x-7)=4 | | 7k-5=-10 | | 2(t-2)+7=-1 | | -2(5a-20)=0 | | -4(3y-1)=-8 | | 3(2a-4)=18 | | 8cos^4x-1=0 | | 3(t+3)=36 | | 0.5y-9=-4 | | 6(x+3-2)=7 | | 6636+c=6638 | | r=4-5 | | x-10*x+10= | | x^3+8x^2+38x-2=0 | | -2.5a-8.9=-2.6-1.8a | | 6.28*7*(x/360)+14=41.8 | | -8+-1=u | | solvex^3+8x^2+38x-2=0 | | 80=-5*t^2+40*t | | m=2-1 | | 6(x+3-2)=64 | | 4x-7+2x+1=180 |

Equations solver categories