15x^2-31x+15=0

Simple and best practice solution for 15x^2-31x+15=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 15x^2-31x+15=0 equation:


Simplifying
15x2 + -31x + 15 = 0

Reorder the terms:
15 + -31x + 15x2 = 0

Solving
15 + -31x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
1 + -2.066666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.066666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.066666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.066666667x + x2 = 0 + -1
-2.066666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.066666667x + x2 = -1

The x term is -2.066666667x.  Take half its coefficient (-1.033333334).
Square it (1.067777779) and add it to both sides.

Add '1.067777779' to each side of the equation.
-2.066666667x + 1.067777779 + x2 = -1 + 1.067777779

Reorder the terms:
1.067777779 + -2.066666667x + x2 = -1 + 1.067777779

Combine like terms: -1 + 1.067777779 = 0.067777779
1.067777779 + -2.066666667x + x2 = 0.067777779

Factor a perfect square on the left side:
(x + -1.033333334)(x + -1.033333334) = 0.067777779

Calculate the square root of the right side: 0.260341658

Break this problem into two subproblems by setting 
(x + -1.033333334) equal to 0.260341658 and -0.260341658.

Subproblem 1

x + -1.033333334 = 0.260341658 Simplifying x + -1.033333334 = 0.260341658 Reorder the terms: -1.033333334 + x = 0.260341658 Solving -1.033333334 + x = 0.260341658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.033333334' to each side of the equation. -1.033333334 + 1.033333334 + x = 0.260341658 + 1.033333334 Combine like terms: -1.033333334 + 1.033333334 = 0.000000000 0.000000000 + x = 0.260341658 + 1.033333334 x = 0.260341658 + 1.033333334 Combine like terms: 0.260341658 + 1.033333334 = 1.293674992 x = 1.293674992 Simplifying x = 1.293674992

Subproblem 2

x + -1.033333334 = -0.260341658 Simplifying x + -1.033333334 = -0.260341658 Reorder the terms: -1.033333334 + x = -0.260341658 Solving -1.033333334 + x = -0.260341658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.033333334' to each side of the equation. -1.033333334 + 1.033333334 + x = -0.260341658 + 1.033333334 Combine like terms: -1.033333334 + 1.033333334 = 0.000000000 0.000000000 + x = -0.260341658 + 1.033333334 x = -0.260341658 + 1.033333334 Combine like terms: -0.260341658 + 1.033333334 = 0.772991676 x = 0.772991676 Simplifying x = 0.772991676

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.293674992, 0.772991676}

See similar equations:

| z^4-z^2-2z+2=0 | | Xy+3x-5y-19=0 | | 4(x+10)+20=20-x | | 9x^2-(y+4x)(y-4x)= | | y^2-8+36=0 | | a+5=2a+3 | | sin(3x+2)-1=-0.5 | | 0.03k+0.05(1000-k)=34 | | 2[(90-x)+(180-x)]+50= | | 7+x+(x+3)=40 | | 7+x+(x+3)= | | 2x+7/3=x-20/6 | | 11w+4+8w=8w+15 | | X^3-4x=15 | | 2(2x-41)=-(x-52) | | 3(90-x)+2(180-x)= | | 15t+4(2t+3)=10-[4t(t-1)] | | y=5cos(2x)-3 | | 3(2x+4)=2x-8 | | a+0+y+d+e=0 | | a+0+y+d+e=0d | | 3(2m+1)= | | 4(y-2)=8-6y | | a+bx=x | | a+bx=6x | | 2x-2y-x^2+y^2= | | 630-5x= | | 4x+2=(-8)+6 | | X^2-13*x-.083=0 | | 5x+147=7x+177 | | 3ln(5-2x)-1=0 | | 24x^2+60x-216=0 |

Equations solver categories