13x=17-x^2

Simple and best practice solution for 13x=17-x^2 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 13x=17-x^2 equation:


Simplifying
13x = 17 + -1x2

Solving
13x = 17 + -1x2

Solving for variable 'x'.

Reorder the terms:
-17 + 13x + x2 = 17 + -1x2 + -17 + x2

Reorder the terms:
-17 + 13x + x2 = 17 + -17 + -1x2 + x2

Combine like terms: 17 + -17 = 0
-17 + 13x + x2 = 0 + -1x2 + x2
-17 + 13x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-17 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 13x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 13x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 13x + x2 = 0 + 17
13x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
13x + x2 = 17

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 17 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 17 + 42.25

Combine like terms: 17 + 42.25 = 59.25
42.25 + 13x + x2 = 59.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 59.25

Calculate the square root of the right side: 7.697402159

Break this problem into two subproblems by setting 
(x + 6.5) equal to 7.697402159 and -7.697402159.

Subproblem 1

x + 6.5 = 7.697402159 Simplifying x + 6.5 = 7.697402159 Reorder the terms: 6.5 + x = 7.697402159 Solving 6.5 + x = 7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.697402159 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.697402159 + -6.5 x = 7.697402159 + -6.5 Combine like terms: 7.697402159 + -6.5 = 1.197402159 x = 1.197402159 Simplifying x = 1.197402159

Subproblem 2

x + 6.5 = -7.697402159 Simplifying x + 6.5 = -7.697402159 Reorder the terms: 6.5 + x = -7.697402159 Solving 6.5 + x = -7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.697402159 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.697402159 + -6.5 x = -7.697402159 + -6.5 Combine like terms: -7.697402159 + -6.5 = -14.197402159 x = -14.197402159 Simplifying x = -14.197402159

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.197402159, -14.197402159}

See similar equations:

| 4(0.5x+7)+5x=15 | | 5m+2=8m-3 | | X+2x+(2x-1.50)= | | ln(x-6)+ln(2)=ln(x) | | 40=5(3w+2) | | 4(2x-7)+x=6x-37 | | D=x+15 | | 2(k+14)= | | 10=8-2a | | -6w+m=-7 | | 2k+7= | | 0.5(x+6)=18 | | 3(x+3)=3x+7 | | 8k+p=-2 | | 54=89-y | | 14x=20-x^2 | | 7x+7=9+5x | | 13x-6+88=27x-2 | | 325=25(d)+50 | | 6x^2+51x-27=0 | | b-b= | | 98+w=210 | | 6x^2+51-27=0 | | 6(f+3)=42 | | 5c+5.8=51.8 | | -8x+9-2x-4=35 | | 5x=9x-36 | | 4y+2= | | 40=2+x(3)-2 | | 0.25(x+30)-0.06(x-10)=-1.4 | | 4(y+1)= | | -4y+3(-3y+5)=-3-6(9-y) |

Equations solver categories