x^2-3x-13=0

Simple and best practice solution for x^2-3x-13=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^2-3x-13=0 equation:


Simplifying
x2 + -3x + -13 = 0

Reorder the terms:
-13 + -3x + x2 = 0

Solving
-13 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -3x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -3x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3x + x2 = 0 + 13
-3x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-3x + x2 = 13

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 13 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 13 + 2.25

Combine like terms: 13 + 2.25 = 15.25
2.25 + -3x + x2 = 15.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

x + -1.5 = 3.905124838 Simplifying x + -1.5 = 3.905124838 Reorder the terms: -1.5 + x = 3.905124838 Solving -1.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.905124838 + 1.5 x = 3.905124838 + 1.5 Combine like terms: 3.905124838 + 1.5 = 5.405124838 x = 5.405124838 Simplifying x = 5.405124838

Subproblem 2

x + -1.5 = -3.905124838 Simplifying x + -1.5 = -3.905124838 Reorder the terms: -1.5 + x = -3.905124838 Solving -1.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.905124838 + 1.5 x = -3.905124838 + 1.5 Combine like terms: -3.905124838 + 1.5 = -2.405124838 x = -2.405124838 Simplifying x = -2.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.405124838, -2.405124838}

See similar equations:

| 25-t=4t | | -8x+5(1-3x)=166 | | x^2-3x-13=o | | -2=3x+4 | | 10=20t-2t^2 | | 3x-5(1-2x)=1 | | 5x+10x-54=66 | | 2n-12-3n=60 | | 34-5(2+p)=9+6(4-9) | | 2(a-4)=4-(2a+4) | | (2x-5)/7=4 | | -2x+5x=4(x-2)-(x-8) | | 6y+6-4y=6 | | (2x-5)/(7)=4 | | -0.9x+2.8=4.1 | | 20t-2t^2=32 | | w+3=6 | | x/7=-9 | | 22t-t^2=117 | | 2L+(2)96=1294 | | -8n-33=3-3(6n-8) | | 4r-9=7 | | y=-3(x-7)2-8 | | -5.5t^2+99t+0=0 | | 6x+5+5x-12=180 | | -5t^2+120t+0=0 | | 5+(p(-3))=-7 | | 2x-y+x+3y=90 | | y=2(x-2)2 | | 5+(p-3)=-7 | | 2n-7=5-4n | | 5+p-3=-7 |

Equations solver categories