2x^2-13x+16=0

Simple and best practice solution for 2x^2-13x+16=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^2-13x+16=0 equation:


Simplifying
2x2 + -13x + 16 = 0

Reorder the terms:
16 + -13x + 2x2 = 0

Solving
16 + -13x + 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'.
8 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -6.5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -6.5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -6.5x + x2 = 0 + -8
-6.5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-6.5x + x2 = -8

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -8 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -8 + 10.5625

Combine like terms: -8 + 10.5625 = 2.5625
10.5625 + -6.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + -3.25) equal to 1.600781059 and -1.600781059.

Subproblem 1

x + -3.25 = 1.600781059 Simplifying x + -3.25 = 1.600781059 Reorder the terms: -3.25 + x = 1.600781059 Solving -3.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 1.600781059 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 1.600781059 + 3.25 x = 1.600781059 + 3.25 Combine like terms: 1.600781059 + 3.25 = 4.850781059 x = 4.850781059 Simplifying x = 4.850781059

Subproblem 2

x + -3.25 = -1.600781059 Simplifying x + -3.25 = -1.600781059 Reorder the terms: -3.25 + x = -1.600781059 Solving -3.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -1.600781059 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -1.600781059 + 3.25 x = -1.600781059 + 3.25 Combine like terms: -1.600781059 + 3.25 = 1.649218941 x = 1.649218941 Simplifying x = 1.649218941

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.850781059, 1.649218941}

See similar equations:

| 3+2(-9n-11)=-2(6+4n)-10n | | 3bm-3= | | (4v-3)(5v-5)= | | 33-10=x | | 33x-15=6x | | 33x-15x=6 | | 8x+12=4x+64 | | 33x+15x=4 | | 12x-65=139 | | 3+6s=4(s-3)+19 | | 2x=5y-43 | | x+(x+1)=63 | | 5(x-4)+x-4=2(8) | | 16x^2-8x-224=0 | | 25x^2-121=0 | | x=180-2x-(16+x) | | 4[2(w-5)]=3[3(w+2)] | | 5x+12=2(1+5x) | | (x+2)2=25 | | 5(8+3r)=r+12 | | 9(n+2)=n+26 | | 5x-1(2X^2+15x+18)=0 | | x+9/5=-3/5 | | 12x(12-2)=12+11x | | +9/5=-3/5 | | 3x-2/12+x=3x+2/3+3 | | (5g-2g)+(2g^2+6g) | | (x-20)+(2x+20)=90 | | 2(s+3)+4s-5=148 | | S+2(s+3)+4s-5=148 | | 7y-987=8 | | 2r^2-9r-4=0 |

Equations solver categories