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Simplifying x3 + -18x2 + -7x = 0 Reorder the terms: -7x + -18x2 + x3 = 0 Solving -7x + -18x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + -18x + 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 '(-7 + -18x + x2)' equal to zero and attempt to solve: Simplifying -7 + -18x + x2 = 0 Solving -7 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -18x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -18x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -18x + x2 = 0 + 7 -18x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -18x + x2 = 7 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 = 7 + 81 Reorder the terms: 81 + -18x + x2 = 7 + 81 Combine like terms: 7 + 81 = 88 81 + -18x + x2 = 88 Factor a perfect square on the left side: (x + -9)(x + -9) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + -9) equal to 9.38083152 and -9.38083152.Subproblem 1
x + -9 = 9.38083152 Simplifying x + -9 = 9.38083152 Reorder the terms: -9 + x = 9.38083152 Solving -9 + x = 9.38083152 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 = 9.38083152 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.38083152 + 9 x = 9.38083152 + 9 Combine like terms: 9.38083152 + 9 = 18.38083152 x = 18.38083152 Simplifying x = 18.38083152Subproblem 2
x + -9 = -9.38083152 Simplifying x + -9 = -9.38083152 Reorder the terms: -9 + x = -9.38083152 Solving -9 + x = -9.38083152 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 = -9.38083152 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.38083152 + 9 x = -9.38083152 + 9 Combine like terms: -9.38083152 + 9 = -0.38083152 x = -0.38083152 Simplifying x = -0.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.38083152, -0.38083152}Solution
x = {0, 18.38083152, -0.38083152}
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