x^2+13x-30=100

Simple and best practice solution for x^2+13x-30=100 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+13x-30=100 equation:


Simplifying
x2 + 13x + -30 = 100

Reorder the terms:
-30 + 13x + x2 = 100

Solving
-30 + 13x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-30 + -100 + 13x + x2 = 100 + -100

Combine like terms: -30 + -100 = -130
-130 + 13x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-130 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 13x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + 13x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 13x + x2 = 0 + 130
13x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
13x + x2 = 130

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 = 130 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 130 + 42.25

Combine like terms: 130 + 42.25 = 172.25
42.25 + 13x + x2 = 172.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 172.25

Calculate the square root of the right side: 13.124404748

Break this problem into two subproblems by setting 
(x + 6.5) equal to 13.124404748 and -13.124404748.

Subproblem 1

x + 6.5 = 13.124404748 Simplifying x + 6.5 = 13.124404748 Reorder the terms: 6.5 + x = 13.124404748 Solving 6.5 + x = 13.124404748 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 = 13.124404748 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 13.124404748 + -6.5 x = 13.124404748 + -6.5 Combine like terms: 13.124404748 + -6.5 = 6.624404748 x = 6.624404748 Simplifying x = 6.624404748

Subproblem 2

x + 6.5 = -13.124404748 Simplifying x + 6.5 = -13.124404748 Reorder the terms: 6.5 + x = -13.124404748 Solving 6.5 + x = -13.124404748 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 = -13.124404748 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -13.124404748 + -6.5 x = -13.124404748 + -6.5 Combine like terms: -13.124404748 + -6.5 = -19.624404748 x = -19.624404748 Simplifying x = -19.624404748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.624404748, -19.624404748}

See similar equations:

| ln(y-6)=ln(y+6)+ln(4) | | 10x^2-x-18=0 | | s-5/s+7 | | 10x^2+x-10=2x+8 | | n^2/2n-8 | | 4x^3-50x^2+145x=120 | | 0=x^4+2y^2+4xy | | y=3x^2-2x-4 | | 2x^3-5x^2+3x=10 | | 1-(1/6z^-1)-(1/3z^-2) | | -5=-65 | | -X-6Y=14 | | (1/4x^4y^8)1/2 | | (0.25x^4y^8)1/2 | | y=(-4.5^2)/10+(9x4.5)/10+11/5 | | n+3/n=19/4 | | 24x+4y-24=0 | | 72x-9y+72=0 | | 72x-9y+72=0fory | | 3y^2+16y-8=0 | | .25*a=5000 | | -(5-10)=5x | | x^2+20x+20=0 | | -5(t+8)=-30 | | d/15=6 | | x+4/7=5/14 | | x^3+y^3= | | 3x+2x-1=18x | | (2x+7/3)-(3x+5/7)+20=30-(3x/5) | | (2x+7/3)-(3x+5/7)-20=30-(3x/5) | | 4a+3b=7 | | 2/x+x/2-2x/3=0 |

Equations solver categories