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Simplifying (6x3 + -6x2 + 4x) + (4x3 + 8x2 + -13x) = 0 Reorder the terms: (4x + -6x2 + 6x3) + (4x3 + 8x2 + -13x) = 0 Remove parenthesis around (4x + -6x2 + 6x3) 4x + -6x2 + 6x3 + (4x3 + 8x2 + -13x) = 0 Reorder the terms: 4x + -6x2 + 6x3 + (-13x + 8x2 + 4x3) = 0 Remove parenthesis around (-13x + 8x2 + 4x3) 4x + -6x2 + 6x3 + -13x + 8x2 + 4x3 = 0 Reorder the terms: 4x + -13x + -6x2 + 8x2 + 6x3 + 4x3 = 0 Combine like terms: 4x + -13x = -9x -9x + -6x2 + 8x2 + 6x3 + 4x3 = 0 Combine like terms: -6x2 + 8x2 = 2x2 -9x + 2x2 + 6x3 + 4x3 = 0 Combine like terms: 6x3 + 4x3 = 10x3 -9x + 2x2 + 10x3 = 0 Solving -9x + 2x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + 2x + 10x2) = 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 '(-9 + 2x + 10x2)' equal to zero and attempt to solve: Simplifying -9 + 2x + 10x2 = 0 Solving -9 + 2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.2x + 0.9 + x2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.2x + x2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.2x + x2 = 0.0 + 0.9 0.2x + x2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 0.2x + x2 = 0.9 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.9 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.9 + 0.01 Combine like terms: 0.9 + 0.01 = 0.91 0.01 + 0.2x + x2 = 0.91 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.91 Calculate the square root of the right side: 0.953939201 Break this problem into two subproblems by setting (x + 0.1) equal to 0.953939201 and -0.953939201.Subproblem 1
x + 0.1 = 0.953939201 Simplifying x + 0.1 = 0.953939201 Reorder the terms: 0.1 + x = 0.953939201 Solving 0.1 + x = 0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.953939201 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.953939201 + -0.1 x = 0.953939201 + -0.1 Combine like terms: 0.953939201 + -0.1 = 0.853939201 x = 0.853939201 Simplifying x = 0.853939201Subproblem 2
x + 0.1 = -0.953939201 Simplifying x + 0.1 = -0.953939201 Reorder the terms: 0.1 + x = -0.953939201 Solving 0.1 + x = -0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.953939201 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.953939201 + -0.1 x = -0.953939201 + -0.1 Combine like terms: -0.953939201 + -0.1 = -1.053939201 x = -1.053939201 Simplifying x = -1.053939201Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.853939201, -1.053939201}Solution
x = {0, 0.853939201, -1.053939201}
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