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Simplifying -1x3 + 18x2 + -25x = 0 Reorder the terms: -25x + 18x2 + -1x3 = 0 Solving -25x + 18x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-25 + 18x + -1x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-25 + 18x + -1x2)' equal to zero and attempt to solve: Simplifying -25 + 18x + -1x2 = 0 Solving -25 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -18x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -18x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -18x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -18x + x2 = 0 + -25 -18x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -18x + x2 = -25 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -25 + 81 Reorder the terms: 81 + -18x + x2 = -25 + 81 Combine like terms: -25 + 81 = 56 81 + -18x + x2 = 56 Factor a perfect square on the left side: (x + -9)(x + -9) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -9) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -9 = 7.483314774 Simplifying x + -9 = 7.483314774 Reorder the terms: -9 + x = 7.483314774 Solving -9 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 7.483314774 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.483314774 + 9 x = 7.483314774 + 9 Combine like terms: 7.483314774 + 9 = 16.483314774 x = 16.483314774 Simplifying x = 16.483314774Subproblem 2
x + -9 = -7.483314774 Simplifying x + -9 = -7.483314774 Reorder the terms: -9 + x = -7.483314774 Solving -9 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -7.483314774 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.483314774 + 9 x = -7.483314774 + 9 Combine like terms: -7.483314774 + 9 = 1.516685226 x = 1.516685226 Simplifying x = 1.516685226Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.483314774, 1.516685226}Solution
x = {0, 16.483314774, 1.516685226}
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