-88x^2+17108x-813360=14000

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Solution for -88x^2+17108x-813360=14000 equation:


Simplifying
-88x2 + 17108x + -813360 = 14000

Reorder the terms:
-813360 + 17108x + -88x2 = 14000

Solving
-813360 + 17108x + -88x2 = 14000

Solving for variable 'x'.

Reorder the terms:
-813360 + -14000 + 17108x + -88x2 = 14000 + -14000

Combine like terms: -813360 + -14000 = -827360
-827360 + 17108x + -88x2 = 14000 + -14000

Combine like terms: 14000 + -14000 = 0
-827360 + 17108x + -88x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-206840 + 4277x + -22x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-206840 + 4277x + -22x2)' equal to zero and attempt to solve: Simplifying -206840 + 4277x + -22x2 = 0 Solving -206840 + 4277x + -22x2 = 0 Begin completing the square. Divide all terms by -22 the coefficient of the squared term: Divide each side by '-22'. 9401.818182 + -194.4090909x + x2 = 0 Move the constant term to the right: Add '-9401.818182' to each side of the equation. 9401.818182 + -194.4090909x + -9401.818182 + x2 = 0 + -9401.818182 Reorder the terms: 9401.818182 + -9401.818182 + -194.4090909x + x2 = 0 + -9401.818182 Combine like terms: 9401.818182 + -9401.818182 = 0.000000 0.000000 + -194.4090909x + x2 = 0 + -9401.818182 -194.4090909x + x2 = 0 + -9401.818182 Combine like terms: 0 + -9401.818182 = -9401.818182 -194.4090909x + x2 = -9401.818182 The x term is -194.4090909x. Take half its coefficient (-97.20454545). Square it (9448.723656) and add it to both sides. Add '9448.723656' to each side of the equation. -194.4090909x + 9448.723656 + x2 = -9401.818182 + 9448.723656 Reorder the terms: 9448.723656 + -194.4090909x + x2 = -9401.818182 + 9448.723656 Combine like terms: -9401.818182 + 9448.723656 = 46.905474 9448.723656 + -194.4090909x + x2 = 46.905474 Factor a perfect square on the left side: (x + -97.20454545)(x + -97.20454545) = 46.905474 Calculate the square root of the right side: 6.848757114 Break this problem into two subproblems by setting (x + -97.20454545) equal to 6.848757114 and -6.848757114.

Subproblem 1

x + -97.20454545 = 6.848757114 Simplifying x + -97.20454545 = 6.848757114 Reorder the terms: -97.20454545 + x = 6.848757114 Solving -97.20454545 + x = 6.848757114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.20454545' to each side of the equation. -97.20454545 + 97.20454545 + x = 6.848757114 + 97.20454545 Combine like terms: -97.20454545 + 97.20454545 = 0.00000000 0.00000000 + x = 6.848757114 + 97.20454545 x = 6.848757114 + 97.20454545 Combine like terms: 6.848757114 + 97.20454545 = 104.053302564 x = 104.053302564 Simplifying x = 104.053302564

Subproblem 2

x + -97.20454545 = -6.848757114 Simplifying x + -97.20454545 = -6.848757114 Reorder the terms: -97.20454545 + x = -6.848757114 Solving -97.20454545 + x = -6.848757114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.20454545' to each side of the equation. -97.20454545 + 97.20454545 + x = -6.848757114 + 97.20454545 Combine like terms: -97.20454545 + 97.20454545 = 0.00000000 0.00000000 + x = -6.848757114 + 97.20454545 x = -6.848757114 + 97.20454545 Combine like terms: -6.848757114 + 97.20454545 = 90.355788336 x = 90.355788336 Simplifying x = 90.355788336

Solution

The solution to the problem is based on the solutions from the subproblems. x = {104.053302564, 90.355788336}

Solution

x = {104.053302564, 90.355788336}

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