28X^2-576X-1296=0

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Solution for 28X^2-576X-1296=0 equation:


Simplifying
28X2 + -576X + -1296 = 0

Reorder the terms:
-1296 + -576X + 28X2 = 0

Solving
-1296 + -576X + 28X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-324 + -144X + 7X2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-324 + -144X + 7X2)' equal to zero and attempt to solve: Simplifying -324 + -144X + 7X2 = 0 Solving -324 + -144X + 7X2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -46.28571429 + -20.57142857X + X2 = 0 Move the constant term to the right: Add '46.28571429' to each side of the equation. -46.28571429 + -20.57142857X + 46.28571429 + X2 = 0 + 46.28571429 Reorder the terms: -46.28571429 + 46.28571429 + -20.57142857X + X2 = 0 + 46.28571429 Combine like terms: -46.28571429 + 46.28571429 = 0.00000000 0.00000000 + -20.57142857X + X2 = 0 + 46.28571429 -20.57142857X + X2 = 0 + 46.28571429 Combine like terms: 0 + 46.28571429 = 46.28571429 -20.57142857X + X2 = 46.28571429 The X term is -20.57142857X. Take half its coefficient (-10.28571429). Square it (105.7959185) and add it to both sides. Add '105.7959185' to each side of the equation. -20.57142857X + 105.7959185 + X2 = 46.28571429 + 105.7959185 Reorder the terms: 105.7959185 + -20.57142857X + X2 = 46.28571429 + 105.7959185 Combine like terms: 46.28571429 + 105.7959185 = 152.08163279 105.7959185 + -20.57142857X + X2 = 152.08163279 Factor a perfect square on the left side: (X + -10.28571429)(X + -10.28571429) = 152.08163279 Calculate the square root of the right side: 12.332138208 Break this problem into two subproblems by setting (X + -10.28571429) equal to 12.332138208 and -12.332138208.

Subproblem 1

X + -10.28571429 = 12.332138208 Simplifying X + -10.28571429 = 12.332138208 Reorder the terms: -10.28571429 + X = 12.332138208 Solving -10.28571429 + X = 12.332138208 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10.28571429' to each side of the equation. -10.28571429 + 10.28571429 + X = 12.332138208 + 10.28571429 Combine like terms: -10.28571429 + 10.28571429 = 0.00000000 0.00000000 + X = 12.332138208 + 10.28571429 X = 12.332138208 + 10.28571429 Combine like terms: 12.332138208 + 10.28571429 = 22.617852498 X = 22.617852498 Simplifying X = 22.617852498

Subproblem 2

X + -10.28571429 = -12.332138208 Simplifying X + -10.28571429 = -12.332138208 Reorder the terms: -10.28571429 + X = -12.332138208 Solving -10.28571429 + X = -12.332138208 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10.28571429' to each side of the equation. -10.28571429 + 10.28571429 + X = -12.332138208 + 10.28571429 Combine like terms: -10.28571429 + 10.28571429 = 0.00000000 0.00000000 + X = -12.332138208 + 10.28571429 X = -12.332138208 + 10.28571429 Combine like terms: -12.332138208 + 10.28571429 = -2.046423918 X = -2.046423918 Simplifying X = -2.046423918

Solution

The solution to the problem is based on the solutions from the subproblems. X = {22.617852498, -2.046423918}

Solution

X = {22.617852498, -2.046423918}

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