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Simplifying 2x3 + -14x2 + -24x = 0 Reorder the terms: -24x + -14x2 + 2x3 = 0 Solving -24x + -14x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-12 + -7x + x2) = 0 Ignore the factor 2.Subproblem 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 '(-12 + -7x + x2)' equal to zero and attempt to solve: Simplifying -12 + -7x + x2 = 0 Solving -12 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -7x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -7x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -7x + x2 = 0 + 12 -7x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -7x + x2 = 12 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 12 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + -7x + x2 = 24.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + -3.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + -3.5 = 4.924428901 Simplifying x + -3.5 = 4.924428901 Reorder the terms: -3.5 + x = 4.924428901 Solving -3.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.924428901 + 3.5 x = 4.924428901 + 3.5 Combine like terms: 4.924428901 + 3.5 = 8.424428901 x = 8.424428901 Simplifying x = 8.424428901Subproblem 2
x + -3.5 = -4.924428901 Simplifying x + -3.5 = -4.924428901 Reorder the terms: -3.5 + x = -4.924428901 Solving -3.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.924428901 + 3.5 x = -4.924428901 + 3.5 Combine like terms: -4.924428901 + 3.5 = -1.424428901 x = -1.424428901 Simplifying x = -1.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.424428901, -1.424428901}Solution
x = {0, 8.424428901, -1.424428901}
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