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Simplifying (3x + 4x2 + 3x3) + (2x + -1x2 + -1x3) + -1(x + 2x2 + 4x3) = 0 Remove parenthesis around (3x + 4x2 + 3x3) 3x + 4x2 + 3x3 + (2x + -1x2 + -1x3) + -1(x + 2x2 + 4x3) = 0 Remove parenthesis around (2x + -1x2 + -1x3) 3x + 4x2 + 3x3 + 2x + -1x2 + -1x3 + -1(x + 2x2 + 4x3) = 0 3x + 4x2 + 3x3 + 2x + -1x2 + -1x3 + (x * -1 + 2x2 * -1 + 4x3 * -1) = 0 3x + 4x2 + 3x3 + 2x + -1x2 + -1x3 + (-1x + -2x2 + -4x3) = 0 Reorder the terms: 3x + 2x + -1x + 4x2 + -1x2 + -2x2 + 3x3 + -1x3 + -4x3 = 0 Combine like terms: 3x + 2x = 5x 5x + -1x + 4x2 + -1x2 + -2x2 + 3x3 + -1x3 + -4x3 = 0 Combine like terms: 5x + -1x = 4x 4x + 4x2 + -1x2 + -2x2 + 3x3 + -1x3 + -4x3 = 0 Combine like terms: 4x2 + -1x2 = 3x2 4x + 3x2 + -2x2 + 3x3 + -1x3 + -4x3 = 0 Combine like terms: 3x2 + -2x2 = 1x2 4x + 1x2 + 3x3 + -1x3 + -4x3 = 0 Combine like terms: 3x3 + -1x3 = 2x3 4x + 1x2 + 2x3 + -4x3 = 0 Combine like terms: 2x3 + -4x3 = -2x3 4x + 1x2 + -2x3 = 0 Solving 4x + 1x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + x + -2x2) = 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 '(4 + x + -2x2)' equal to zero and attempt to solve: Simplifying 4 + x + -2x2 = 0 Solving 4 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2 + -0.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.5x + x2 = 0 + 2 -0.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.5x + x2 = 2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = 2 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = 2 + 0.25 Combine like terms: 2 + 0.25 = 2.25 0.25 + -0.5x + x2 = 2.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 0.5) equal to 1.5 and -1.5.Subproblem 1
x + 0.5 = 1.5 Simplifying x + 0.5 = 1.5 Reorder the terms: 0.5 + x = 1.5 Solving 0.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.5 + -0.5 x = 1.5 + -0.5 Combine like terms: 1.5 + -0.5 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 0.5 = -1.5 Simplifying x + 0.5 = -1.5 Reorder the terms: 0.5 + x = -1.5 Solving 0.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.5 + -0.5 x = -1.5 + -0.5 Combine like terms: -1.5 + -0.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -2}Solution
x = {0, 1, -2}
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