-4x^2+70x+6000=0

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Solution for -4x^2+70x+6000=0 equation: 


Simplifying
-4x2 + 70x + 6000 = 0

Reorder the terms:
6000 + 70x + -4x2 = 0

Solving
6000 + 70x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3000 + 35x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3000 + 35x + -2x2)' equal to zero and attempt to solve:

Simplifying
3000 + 35x + -2x2 = 0

Solving
3000 + 35x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1500 + -17.5x + x2 = 0

Move the constant term to the right:

Add '1500' to each side of the equation.
-1500 + -17.5x + 1500 + x2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + -17.5x + x2 = 0 + 1500

Combine like terms: -1500 + 1500 = 0
0 + -17.5x + x2 = 0 + 1500
-17.5x + x2 = 0 + 1500

Combine like terms: 0 + 1500 = 1500
-17.5x + x2 = 1500

The x term is -17.5x.  Take half its coefficient (-8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
-17.5x + 76.5625 + x2 = 1500 + 76.5625

Reorder the terms:
76.5625 + -17.5x + x2 = 1500 + 76.5625

Combine like terms: 1500 + 76.5625 = 1576.5625
76.5625 + -17.5x + x2 = 1576.5625

Factor a perfect square on the left side:
(x + -8.75)(x + -8.75) = 1576.5625

Calculate the square root of the right side: 39.705950436

Break this problem into two subproblems by setting 
(x + -8.75) equal to 39.705950436 and -39.705950436.


Subproblem 1
x + -8.75 = 39.705950436

Simplifying
x + -8.75 = 39.705950436

Reorder the terms:
-8.75 + x = 39.705950436

Solving
-8.75 + x = 39.705950436

Solving for variable 'x'.

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

Add '8.75' to each side of the equation.
-8.75 + 8.75 + x = 39.705950436 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = 39.705950436 + 8.75
x = 39.705950436 + 8.75

Combine like terms: 39.705950436 + 8.75 = 48.455950436
x = 48.455950436

Simplifying
x = 48.455950436


Subproblem 2
x + -8.75 = -39.705950436

Simplifying
x + -8.75 = -39.705950436

Reorder the terms:
-8.75 + x = -39.705950436

Solving
-8.75 + x = -39.705950436

Solving for variable 'x'.

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

Add '8.75' to each side of the equation.
-8.75 + 8.75 + x = -39.705950436 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = -39.705950436 + 8.75
x = -39.705950436 + 8.75

Combine like terms: -39.705950436 + 8.75 = -30.955950436
x = -30.955950436

Simplifying
x = -30.955950436


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.455950436, -30.955950436}
Solution
x = {48.455950436, -30.955950436}

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