4x^2-x-13=0

Simple and best practice solution for 4x^2-x-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 4x^2-x-13=0 equation:


Simplifying
4x2 + -1x + -13 = 0

Reorder the terms:
-13 + -1x + 4x2 = 0

Solving
-13 + -1x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-3.25 + -0.25x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -0.25x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -0.25x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -0.25x + x2 = 0 + 3.25
-0.25x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-0.25x + x2 = 3.25

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 3.25 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 3.25 + 0.015625

Combine like terms: 3.25 + 0.015625 = 3.265625
0.015625 + -0.25x + x2 = 3.265625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 3.265625

Calculate the square root of the right side: 1.807104037

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.807104037 and -1.807104037.

Subproblem 1

x + -0.125 = 1.807104037 Simplifying x + -0.125 = 1.807104037 Reorder the terms: -0.125 + x = 1.807104037 Solving -0.125 + x = 1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.807104037 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.807104037 + 0.125 x = 1.807104037 + 0.125 Combine like terms: 1.807104037 + 0.125 = 1.932104037 x = 1.932104037 Simplifying x = 1.932104037

Subproblem 2

x + -0.125 = -1.807104037 Simplifying x + -0.125 = -1.807104037 Reorder the terms: -0.125 + x = -1.807104037 Solving -0.125 + x = -1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.807104037 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.807104037 + 0.125 x = -1.807104037 + 0.125 Combine like terms: -1.807104037 + 0.125 = -1.682104037 x = -1.682104037 Simplifying x = -1.682104037

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.932104037, -1.682104037}

See similar equations:

| 8-3(2-x)=20 | | 17=3[p-5]+8 | | 8/35x=-16/21 | | 4/r+9/r-7 | | 9x-12=-5x | | w^2+5w-126=0 | | -2x+7=-53 | | 2(4+5x)-3(x-1)=-22 | | 8x-10+2x^2=0 | | 10a=20+r | | 2[x+3]=10 | | 3/4x-1/2x-4=12 | | 125=50t | | (x)=27+0.40x | | 2y-2+3y-6=10 | | -4(x+7)=-15 | | 2f=4f-6 | | 7c-25=65 | | 15.5=2.7n+2 | | 68=5x+43 | | B+T+TB=320 | | 3v-9=7+3v-v | | -x-3-2=2x+5 | | 0.5x+1.3=0.9x-0.7 | | 5[h-4]=8 | | 7c+25=65 | | 2.4x+1.2x-6.5=0.7 | | 6=-2[7-c] | | 2.1n-1.1n+2.2=6.6+0.7 | | 15.5=2.7+2 | | 1-4x=3x+10 | | 7c+65=65 |

Equations solver categories