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Simplifying (3x3 + -5x2 + 5x) + (5x3 + 9x2 + -12x) = 0 Reorder the terms: (5x + -5x2 + 3x3) + (5x3 + 9x2 + -12x) = 0 Remove parenthesis around (5x + -5x2 + 3x3) 5x + -5x2 + 3x3 + (5x3 + 9x2 + -12x) = 0 Reorder the terms: 5x + -5x2 + 3x3 + (-12x + 9x2 + 5x3) = 0 Remove parenthesis around (-12x + 9x2 + 5x3) 5x + -5x2 + 3x3 + -12x + 9x2 + 5x3 = 0 Reorder the terms: 5x + -12x + -5x2 + 9x2 + 3x3 + 5x3 = 0 Combine like terms: 5x + -12x = -7x -7x + -5x2 + 9x2 + 3x3 + 5x3 = 0 Combine like terms: -5x2 + 9x2 = 4x2 -7x + 4x2 + 3x3 + 5x3 = 0 Combine like terms: 3x3 + 5x3 = 8x3 -7x + 4x2 + 8x3 = 0 Solving -7x + 4x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 4x + 8x2) = 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 + 4x + 8x2)' equal to zero and attempt to solve: Simplifying -7 + 4x + 8x2 = 0 Solving -7 + 4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.5x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.5x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.5x + x2 = 0 + 0.875 0.5x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.5x + x2 = 0.875 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.875 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.875 + 0.0625 Combine like terms: 0.875 + 0.0625 = 0.9375 0.0625 + 0.5x + x2 = 0.9375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.9375 Calculate the square root of the right side: 0.968245837 Break this problem into two subproblems by setting (x + 0.25) equal to 0.968245837 and -0.968245837.Subproblem 1
x + 0.25 = 0.968245837 Simplifying x + 0.25 = 0.968245837 Reorder the terms: 0.25 + x = 0.968245837 Solving 0.25 + x = 0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.968245837 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.968245837 + -0.25 x = 0.968245837 + -0.25 Combine like terms: 0.968245837 + -0.25 = 0.718245837 x = 0.718245837 Simplifying x = 0.718245837Subproblem 2
x + 0.25 = -0.968245837 Simplifying x + 0.25 = -0.968245837 Reorder the terms: 0.25 + x = -0.968245837 Solving 0.25 + x = -0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.968245837 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.968245837 + -0.25 x = -0.968245837 + -0.25 Combine like terms: -0.968245837 + -0.25 = -1.218245837 x = -1.218245837 Simplifying x = -1.218245837Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.718245837, -1.218245837}Solution
x = {0, 0.718245837, -1.218245837}
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