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Simplifying 256x2 + -6561x + 256 = 0 Reorder the terms: 256 + -6561x + 256x2 = 0 Solving 256 + -6561x + 256x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 256 the coefficient of the squared term: Divide each side by '256'. 1 + -25.62890625x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -25.62890625x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -25.62890625x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -25.62890625x + x2 = 0 + -1 -25.62890625x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -25.62890625x + x2 = -1 The x term is -25.62890625x. Take half its coefficient (-12.81445313). Square it (164.2102090) and add it to both sides. Add '164.2102090' to each side of the equation. -25.62890625x + 164.2102090 + x2 = -1 + 164.2102090 Reorder the terms: 164.2102090 + -25.62890625x + x2 = -1 + 164.2102090 Combine like terms: -1 + 164.2102090 = 163.210209 164.2102090 + -25.62890625x + x2 = 163.210209 Factor a perfect square on the left side: (x + -12.81445313)(x + -12.81445313) = 163.210209 Calculate the square root of the right side: 12.775375102 Break this problem into two subproblems by setting (x + -12.81445313) equal to 12.775375102 and -12.775375102.Subproblem 1
x + -12.81445313 = 12.775375102 Simplifying x + -12.81445313 = 12.775375102 Reorder the terms: -12.81445313 + x = 12.775375102 Solving -12.81445313 + x = 12.775375102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.81445313' to each side of the equation. -12.81445313 + 12.81445313 + x = 12.775375102 + 12.81445313 Combine like terms: -12.81445313 + 12.81445313 = 0.00000000 0.00000000 + x = 12.775375102 + 12.81445313 x = 12.775375102 + 12.81445313 Combine like terms: 12.775375102 + 12.81445313 = 25.589828232 x = 25.589828232 Simplifying x = 25.589828232Subproblem 2
x + -12.81445313 = -12.775375102 Simplifying x + -12.81445313 = -12.775375102 Reorder the terms: -12.81445313 + x = -12.775375102 Solving -12.81445313 + x = -12.775375102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.81445313' to each side of the equation. -12.81445313 + 12.81445313 + x = -12.775375102 + 12.81445313 Combine like terms: -12.81445313 + 12.81445313 = 0.00000000 0.00000000 + x = -12.775375102 + 12.81445313 x = -12.775375102 + 12.81445313 Combine like terms: -12.775375102 + 12.81445313 = 0.039078028 x = 0.039078028 Simplifying x = 0.039078028Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.589828232, 0.039078028}
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