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Simplifying x3 = 18x + -5x2 Solving x3 = 18x + -5x2 Solving for variable 'x'. Reorder the terms: -18x + 5x2 + x3 = 18x + -5x2 + -18x + 5x2 Reorder the terms: -18x + 5x2 + x3 = 18x + -18x + -5x2 + 5x2 Combine like terms: 18x + -18x = 0 -18x + 5x2 + x3 = 0 + -5x2 + 5x2 -18x + 5x2 + x3 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -18x + 5x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-18 + 5x + x2) = 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 '(-18 + 5x + x2)' equal to zero and attempt to solve: Simplifying -18 + 5x + x2 = 0 Solving -18 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 5x + x2 = 0 + 18 5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 5x + x2 = 18 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 18 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 18 + 6.25 Combine like terms: 18 + 6.25 = 24.25 6.25 + 5x + x2 = 24.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 2.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 2.5 = 4.924428901 Simplifying x + 2.5 = 4.924428901 Reorder the terms: 2.5 + x = 4.924428901 Solving 2.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.924428901 + -2.5 x = 4.924428901 + -2.5 Combine like terms: 4.924428901 + -2.5 = 2.424428901 x = 2.424428901 Simplifying x = 2.424428901Subproblem 2
x + 2.5 = -4.924428901 Simplifying x + 2.5 = -4.924428901 Reorder the terms: 2.5 + x = -4.924428901 Solving 2.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.924428901 + -2.5 x = -4.924428901 + -2.5 Combine like terms: -4.924428901 + -2.5 = -7.424428901 x = -7.424428901 Simplifying x = -7.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.424428901, -7.424428901}Solution
x = {0, 2.424428901, -7.424428901}
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