x=x^2+10x-75

Simple and best practice solution for x=x^2+10x-75 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=x^2+10x-75 equation:


Simplifying
x = x2 + 10x + -75

Reorder the terms:
x = -75 + 10x + x2

Solving
x = -75 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
75 + x + -10x + -1x2 = -75 + 10x + x2 + 75 + -10x + -1x2

Combine like terms: x + -10x = -9x
75 + -9x + -1x2 = -75 + 10x + x2 + 75 + -10x + -1x2

Reorder the terms:
75 + -9x + -1x2 = -75 + 75 + 10x + -10x + x2 + -1x2

Combine like terms: -75 + 75 = 0
75 + -9x + -1x2 = 0 + 10x + -10x + x2 + -1x2
75 + -9x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
75 + -9x + -1x2 = 0 + x2 + -1x2
75 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
75 + -9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-75 + 9x + x2 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 9x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 9x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 9x + x2 = 0 + 75
9x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
9x + x2 = 75

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 75 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 75 + 20.25

Combine like terms: 75 + 20.25 = 95.25
20.25 + 9x + x2 = 95.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 95.25

Calculate the square root of the right side: 9.759610648

Break this problem into two subproblems by setting 
(x + 4.5) equal to 9.759610648 and -9.759610648.

Subproblem 1

x + 4.5 = 9.759610648 Simplifying x + 4.5 = 9.759610648 Reorder the terms: 4.5 + x = 9.759610648 Solving 4.5 + x = 9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 9.759610648 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.759610648 + -4.5 x = 9.759610648 + -4.5 Combine like terms: 9.759610648 + -4.5 = 5.259610648 x = 5.259610648 Simplifying x = 5.259610648

Subproblem 2

x + 4.5 = -9.759610648 Simplifying x + 4.5 = -9.759610648 Reorder the terms: 4.5 + x = -9.759610648 Solving 4.5 + x = -9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -9.759610648 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.759610648 + -4.5 x = -9.759610648 + -4.5 Combine like terms: -9.759610648 + -4.5 = -14.259610648 x = -14.259610648 Simplifying x = -14.259610648

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.259610648, -14.259610648}

See similar equations:

| 2(t+12)-6(2t+3)=14 | | y-10+5y=9y-8 | | 9n-4=4(n-2)-5n+4 | | 5m+6=16 | | 5m+6=14 | | 12m-9-10m+3-2m=10-3m+9 | | 2x+5y-(7x+8y)= | | 2t-(5-t)=13+2t | | 10x+5y=90 | | 31-2z=15 | | 7x-13=6x+3 | | 8x-5+7x-10=7x-20 | | 9-7x=2x+90 | | 7-6a=-5 | | 2-7y=13 | | x^2+1=x^2+4+x^2+9 | | 4x-16=1x-16 | | z=2x-3-7 | | 50=3x+x | | z=2-3-7 | | 25x+5y+1=0 | | 4b=6 | | 7h+21+4=-3 | | x+13,5+x+13,5+x=180 | | 45x+52=38 | | 0=2x^3+16x^2+30 | | -4y+11x=8 | | 4x-y=45 | | 63-6x=7x+4 | | 0=2x^3+8x^2+6x | | 59x+1=60 | | y^4-36y^2-1296=0 |

Equations solver categories