2x^2-7x-13=0

Simple and best practice solution for 2x^2-7x-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 2x^2-7x-13=0 equation:


Simplifying
2x2 + -7x + -13 = 0

Reorder the terms:
-13 + -7x + 2x2 = 0

Solving
-13 + -7x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-6.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -3.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -3.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -3.5x + x2 = 0 + 6.5
-3.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-3.5x + x2 = 6.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 6.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 6.5 + 3.0625

Combine like terms: 6.5 + 3.0625 = 9.5625
3.0625 + -3.5x + x2 = 9.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(x + -1.75) equal to 3.092329219 and -3.092329219.

Subproblem 1

x + -1.75 = 3.092329219 Simplifying x + -1.75 = 3.092329219 Reorder the terms: -1.75 + x = 3.092329219 Solving -1.75 + x = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.092329219 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.092329219 + 1.75 x = 3.092329219 + 1.75 Combine like terms: 3.092329219 + 1.75 = 4.842329219 x = 4.842329219 Simplifying x = 4.842329219

Subproblem 2

x + -1.75 = -3.092329219 Simplifying x + -1.75 = -3.092329219 Reorder the terms: -1.75 + x = -3.092329219 Solving -1.75 + x = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.092329219 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.092329219 + 1.75 x = -3.092329219 + 1.75 Combine like terms: -3.092329219 + 1.75 = -1.342329219 x = -1.342329219 Simplifying x = -1.342329219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.842329219, -1.342329219}

See similar equations:

| 4=.5(-5)+b | | 3x-8+26=30 | | m^2-8m+16=7 | | 2x-9x+3=3-6-5x | | 0=4x^2-16 | | 5c-10d+cx-2dx= | | 100x^2+49=0 | | -3(t-5)+2(7+2t)=36 | | y^2-2y-3y+6= | | 2x+6y=7 | | 2y-4+8y=7y-8+3y | | 2x-8=-4-6x | | 6x+4-18=28 | | (7x+5)(x+3)=0 | | 5x-8=2(x-1) | | 2m+n=10 | | 12x^2+7x+5=4 | | t=2n+2u | | X(20x+19)=28 | | 9x+9=9(x+5)-5 | | 0.06x=300 | | 5k=24+3k | | b+1.5=2 | | 45=t+8t | | 96a^2+336a+294= | | 15x^2+24x=0 | | 3x^2+6=10x | | 3i-4=5i+13 | | 5x+13=23 | | 3x^2+10x-77=0 | | d-3=-25 | | c=zt+z |

Equations solver categories