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Simplifying 3x3 + -12x2 + -45x = 0 Reorder the terms: -45x + -12x2 + 3x3 = 0 Solving -45x + -12x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-15 + -4x + x2) = 0 Ignore the factor 3.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 '(-15 + -4x + x2)' equal to zero and attempt to solve: Simplifying -15 + -4x + x2 = 0 Solving -15 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -4x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -4x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4x + x2 = 0 + 15 -4x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4x + x2 = 15 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 15 + 4 Reorder the terms: 4 + -4x + x2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4x + x2 = 19 Factor a perfect square on the left side: (x + -2)(x + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -2 = 4.358898944 Simplifying x + -2 = 4.358898944 Reorder the terms: -2 + x = 4.358898944 Solving -2 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.358898944 + 2 x = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 x = 6.358898944 Simplifying x = 6.358898944Subproblem 2
x + -2 = -4.358898944 Simplifying x + -2 = -4.358898944 Reorder the terms: -2 + x = -4.358898944 Solving -2 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.358898944 + 2 x = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 x = -2.358898944 Simplifying x = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.358898944, -2.358898944}Solution
x = {0, 6.358898944, -2.358898944}
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