x^2-x-31=0

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


Simplifying
x2 + -1x + -31 = 0

Reorder the terms:
-31 + -1x + x2 = 0

Solving
-31 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -1x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -1x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1x + x2 = 0 + 31
-1x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-1x + x2 = 31

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 31 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 31 + 0.25

Combine like terms: 31 + 0.25 = 31.25
0.25 + -1x + x2 = 31.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.590169944 and -5.590169944.

Subproblem 1

x + -0.5 = 5.590169944 Simplifying x + -0.5 = 5.590169944 Reorder the terms: -0.5 + x = 5.590169944 Solving -0.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.590169944 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.590169944 + 0.5 x = 5.590169944 + 0.5 Combine like terms: 5.590169944 + 0.5 = 6.090169944 x = 6.090169944 Simplifying x = 6.090169944

Subproblem 2

x + -0.5 = -5.590169944 Simplifying x + -0.5 = -5.590169944 Reorder the terms: -0.5 + x = -5.590169944 Solving -0.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.590169944 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.590169944 + 0.5 x = -5.590169944 + 0.5 Combine like terms: -5.590169944 + 0.5 = -5.090169944 x = -5.090169944 Simplifying x = -5.090169944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.090169944, -5.090169944}

See similar equations:

| 30=5(x-6) | | 17x-5y=-29 | | 7.5p=45 | | (x^2-4x-5)(x^2+6x+5)= | | 10(x+2)=-2(6+-9x) | | 3x=4-y | | 4125c+5000=-9850 | | 3(-4x+12)=-6(x-3) | | 5x-2y+7y-3x= | | 4.125c+5=-9.4 | | 1*x=8+4-10+1 | | 3(17)-7= | | (X-8y)(x+8y)= | | 6-4n=7n-9n-8 | | 13n=91 | | -5n+6=-2(8n-1) | | 3x+5-4x=2x+2 | | d-2.7=-2.0 | | 9y-12=33 | | -15+c=75 | | -11(2x+7)=-33 | | 9(2x+3)=-36-27(1x+2) | | -2x-y=9 | | 9+2(5y+8)=-5 | | 2x=6(x-24) | | 2(3-4x)=4+4(6-1x) | | 6x+5x+2+7=6x+4+4x | | 228=x+(2x-63) | | 1+3x-4+2x=3 | | 2(1-1x)=3(1x+9) | | x+7y=-14 | | -1(3+7x)=3(x+5)-8 |

Equations solver categories