6x^2+10x-9=0

Simple and best practice solution for 6x^2+10x-9=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 6x^2+10x-9=0 equation:


Simplifying
6x2 + 10x + -9 = 0

Reorder the terms:
-9 + 10x + 6x2 = 0

Solving
-9 + 10x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-1.5 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.666666667x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.666666667x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.666666667x + x2 = 0 + 1.5
1.666666667x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.666666667x + x2 = 1.5

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 1.5 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 1.5 + 0.6944444447

Combine like terms: 1.5 + 0.6944444447 = 2.1944444447
0.6944444447 + 1.666666667x + x2 = 2.1944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 2.1944444447

Calculate the square root of the right side: 1.481365736

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.481365736 and -1.481365736.

Subproblem 1

x + 0.8333333335 = 1.481365736 Simplifying x + 0.8333333335 = 1.481365736 Reorder the terms: 0.8333333335 + x = 1.481365736 Solving 0.8333333335 + x = 1.481365736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.481365736 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.481365736 + -0.8333333335 x = 1.481365736 + -0.8333333335 Combine like terms: 1.481365736 + -0.8333333335 = 0.6480324025 x = 0.6480324025 Simplifying x = 0.6480324025

Subproblem 2

x + 0.8333333335 = -1.481365736 Simplifying x + 0.8333333335 = -1.481365736 Reorder the terms: 0.8333333335 + x = -1.481365736 Solving 0.8333333335 + x = -1.481365736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.481365736 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.481365736 + -0.8333333335 x = -1.481365736 + -0.8333333335 Combine like terms: -1.481365736 + -0.8333333335 = -2.3146990695 x = -2.3146990695 Simplifying x = -2.3146990695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6480324025, -2.3146990695}

See similar equations:

| (X-4)2+5=30 | | 5t-3=3t+10 | | 20x+2x=40000 | | 14x-8x^2=0 | | 9(2y-3)-(6y+7)= | | -3z(4z^2-4)=0 | | 20x-1=37x+1 | | -(3s+4t)+(-s-4t)= | | 6x-15=7x-20 | | 3x+8=-7x+6 | | z^2-6x+9=0 | | n=70+y | | 57+10x=111-2x | | 6s-16=80 | | 5x+5=4x+11 | | 60=3107n | | 7.5/.8 | | 7+4x=4+x | | -28n+14n+33=-23 | | X+14=3x+18 | | kx^2-(3k+2)x+7=0 | | Z+10=0 | | 18y-2+10x=180 | | (5x-12)(5x-1)= | | z+10=10 | | 5x+1=11x-6 | | 9x-20-x^2=0 | | 13x^2+12x+2=0 | | 4(2-3)=52 | | 10x-21-x^2=0 | | 7x-60+3x+110=180 | | 1/9*-5^2 |

Equations solver categories