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Simplifying 4x3 + -5x + 3x2 + 6x2 + -5x3 + -1x = 0 Reorder the terms: -5x + -1x + 3x2 + 6x2 + 4x3 + -5x3 = 0 Combine like terms: -5x + -1x = -6x -6x + 3x2 + 6x2 + 4x3 + -5x3 = 0 Combine like terms: 3x2 + 6x2 = 9x2 -6x + 9x2 + 4x3 + -5x3 = 0 Combine like terms: 4x3 + -5x3 = -1x3 -6x + 9x2 + -1x3 = 0 Solving -6x + 9x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 9x + -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 '(-6 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying -6 + 9x + -1x2 = 0 Solving -6 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -9x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -9x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9x + x2 = 0 + -6 -9x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9x + x2 = -6 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -6 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + -9x + x2 = 14.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -4.5 = 3.774917218 Simplifying x + -4.5 = 3.774917218 Reorder the terms: -4.5 + x = 3.774917218 Solving -4.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.774917218 + 4.5 x = 3.774917218 + 4.5 Combine like terms: 3.774917218 + 4.5 = 8.274917218 x = 8.274917218 Simplifying x = 8.274917218Subproblem 2
x + -4.5 = -3.774917218 Simplifying x + -4.5 = -3.774917218 Reorder the terms: -4.5 + x = -3.774917218 Solving -4.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.774917218 + 4.5 x = -3.774917218 + 4.5 Combine like terms: -3.774917218 + 4.5 = 0.725082782 x = 0.725082782 Simplifying x = 0.725082782Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.274917218, 0.725082782}Solution
x = {0, 8.274917218, 0.725082782}
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