0=7X^2-253X-1700

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Solution for 0=7X^2-253X-1700 equation:


Simplifying
0 = 7X2 + -253X + -1700

Reorder the terms:
0 = -1700 + -253X + 7X2

Solving
0 = -1700 + -253X + 7X2

Solving for variable 'X'.

Combine like terms: 0 + 1700 = 1700
1700 + 253X + -7X2 = -1700 + -253X + 7X2 + 1700 + 253X + -7X2

Reorder the terms:
1700 + 253X + -7X2 = -1700 + 1700 + -253X + 253X + 7X2 + -7X2

Combine like terms: -1700 + 1700 = 0
1700 + 253X + -7X2 = 0 + -253X + 253X + 7X2 + -7X2
1700 + 253X + -7X2 = -253X + 253X + 7X2 + -7X2

Combine like terms: -253X + 253X = 0
1700 + 253X + -7X2 = 0 + 7X2 + -7X2
1700 + 253X + -7X2 = 7X2 + -7X2

Combine like terms: 7X2 + -7X2 = 0
1700 + 253X + -7X2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-242.8571429 + -36.14285714X + X2 = 0

Move the constant term to the right:

Add '242.8571429' to each side of the equation.
-242.8571429 + -36.14285714X + 242.8571429 + X2 = 0 + 242.8571429

Reorder the terms:
-242.8571429 + 242.8571429 + -36.14285714X + X2 = 0 + 242.8571429

Combine like terms: -242.8571429 + 242.8571429 = 0.0000000
0.0000000 + -36.14285714X + X2 = 0 + 242.8571429
-36.14285714X + X2 = 0 + 242.8571429

Combine like terms: 0 + 242.8571429 = 242.8571429
-36.14285714X + X2 = 242.8571429

The X term is -36.14285714X.  Take half its coefficient (-18.07142857).
Square it (326.5765306) and add it to both sides.

Add '326.5765306' to each side of the equation.
-36.14285714X + 326.5765306 + X2 = 242.8571429 + 326.5765306

Reorder the terms:
326.5765306 + -36.14285714X + X2 = 242.8571429 + 326.5765306

Combine like terms: 242.8571429 + 326.5765306 = 569.4336735
326.5765306 + -36.14285714X + X2 = 569.4336735

Factor a perfect square on the left side:
(X + -18.07142857)(X + -18.07142857) = 569.4336735

Calculate the square root of the right side: 23.862809422

Break this problem into two subproblems by setting 
(X + -18.07142857) equal to 23.862809422 and -23.862809422.

Subproblem 1

X + -18.07142857 = 23.862809422 Simplifying X + -18.07142857 = 23.862809422 Reorder the terms: -18.07142857 + X = 23.862809422 Solving -18.07142857 + X = 23.862809422 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '18.07142857' to each side of the equation. -18.07142857 + 18.07142857 + X = 23.862809422 + 18.07142857 Combine like terms: -18.07142857 + 18.07142857 = 0.00000000 0.00000000 + X = 23.862809422 + 18.07142857 X = 23.862809422 + 18.07142857 Combine like terms: 23.862809422 + 18.07142857 = 41.934237992 X = 41.934237992 Simplifying X = 41.934237992

Subproblem 2

X + -18.07142857 = -23.862809422 Simplifying X + -18.07142857 = -23.862809422 Reorder the terms: -18.07142857 + X = -23.862809422 Solving -18.07142857 + X = -23.862809422 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '18.07142857' to each side of the equation. -18.07142857 + 18.07142857 + X = -23.862809422 + 18.07142857 Combine like terms: -18.07142857 + 18.07142857 = 0.00000000 0.00000000 + X = -23.862809422 + 18.07142857 X = -23.862809422 + 18.07142857 Combine like terms: -23.862809422 + 18.07142857 = -5.791380852 X = -5.791380852 Simplifying X = -5.791380852

Solution

The solution to the problem is based on the solutions from the subproblems. X = {41.934237992, -5.791380852}

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