-100x^2+2500x+1000=12500

Simple and best practice solution for -100x^2+2500x+1000=12500 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 -100x^2+2500x+1000=12500 equation: 


Simplifying
-100x2 + 2500x + 1000 = 12500

Reorder the terms:
1000 + 2500x + -100x2 = 12500

Solving
1000 + 2500x + -100x2 = 12500

Solving for variable 'x'.

Reorder the terms:
1000 + -12500 + 2500x + -100x2 = 12500 + -12500

Combine like terms: 1000 + -12500 = -11500
-11500 + 2500x + -100x2 = 12500 + -12500

Combine like terms: 12500 + -12500 = 0
-11500 + 2500x + -100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(-115 + 25x + -1x2) = 0

Ignore the factor 100.

Subproblem 1
Set the factor '(-115 + 25x + -1x2)' equal to zero and attempt to solve:

Simplifying
-115 + 25x + -1x2 = 0

Solving
-115 + 25x + -1x2 = 0

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

Divide each side by '-1'.
115 + -25x + x2 = 0

Move the constant term to the right:

Add '-115' to each side of the equation.
115 + -25x + -115 + x2 = 0 + -115

Reorder the terms:
115 + -115 + -25x + x2 = 0 + -115

Combine like terms: 115 + -115 = 0
0 + -25x + x2 = 0 + -115
-25x + x2 = 0 + -115

Combine like terms: 0 + -115 = -115
-25x + x2 = -115

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -115 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -115 + 156.25

Combine like terms: -115 + 156.25 = 41.25
156.25 + -25x + x2 = 41.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + -12.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
x + -12.5 = 6.422616289

Simplifying
x + -12.5 = 6.422616289

Reorder the terms:
-12.5 + x = 6.422616289

Solving
-12.5 + x = 6.422616289

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 6.422616289 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 6.422616289 + 12.5
x = 6.422616289 + 12.5

Combine like terms: 6.422616289 + 12.5 = 18.922616289
x = 18.922616289

Simplifying
x = 18.922616289


Subproblem 2
x + -12.5 = -6.422616289

Simplifying
x + -12.5 = -6.422616289

Reorder the terms:
-12.5 + x = -6.422616289

Solving
-12.5 + x = -6.422616289

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -6.422616289 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -6.422616289 + 12.5
x = -6.422616289 + 12.5

Combine like terms: -6.422616289 + 12.5 = 6.077383711
x = 6.077383711

Simplifying
x = 6.077383711


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.922616289, 6.077383711}
Solution
x = {18.922616289, 6.077383711}

See similar equations:

| 6v+9=-7 | | k^2-14k+28=k^2-12k+36 | | log[4](3x+2)=log[4](2x+5) | | n^2-7n+16=n^2+8n+16 | | -2p+4+3p=7 | | (-2/5)t=-8 | | -2/5t=-8 | | z+3=-15 | | |19/4|= | | 212/1.06 | | -r^2-8r+65= | | y=1/6x2 | | =-3x^2-2x+2 | | (5x+27)(3x+17)=0 | | x^2+25+10=125 | | x^4+51x^2-4900=0 | | 81-3x=x^2+18x+81 | | 1/x:1/5=1/x:1/125 | | 3x/2-2x/5=7 | | 21/x-6-81/x-1 | | =-16x^2+215x-95 | | 4x^2=11x | | -[6z-(17z+9)]=9+(10z+2) | | (-6x^2-60x)= | | 3(x+1)=4-(2x-3) | | (-x^2-60x)= | | -(3-(x-2))=-5 | | 5-3/5y-10 | | 6(x-1)+3x= | | 2(4x+2)-3(2-6x)=63 | | -7x+4y=-3 | | 5x+32=11x-0 |

Equations solver categories