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Simplifying (3x3 + -4x2 + 7x) + (4x3 + 9x2 + -12x) = 0 Reorder the terms: (7x + -4x2 + 3x3) + (4x3 + 9x2 + -12x) = 0 Remove parenthesis around (7x + -4x2 + 3x3) 7x + -4x2 + 3x3 + (4x3 + 9x2 + -12x) = 0 Reorder the terms: 7x + -4x2 + 3x3 + (-12x + 9x2 + 4x3) = 0 Remove parenthesis around (-12x + 9x2 + 4x3) 7x + -4x2 + 3x3 + -12x + 9x2 + 4x3 = 0 Reorder the terms: 7x + -12x + -4x2 + 9x2 + 3x3 + 4x3 = 0 Combine like terms: 7x + -12x = -5x -5x + -4x2 + 9x2 + 3x3 + 4x3 = 0 Combine like terms: -4x2 + 9x2 = 5x2 -5x + 5x2 + 3x3 + 4x3 = 0 Combine like terms: 3x3 + 4x3 = 7x3 -5x + 5x2 + 7x3 = 0 Solving -5x + 5x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 5x + 7x2) = 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 '(-5 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying -5 + 5x + 7x2 = 0 Solving -5 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.7142857143x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.7142857143x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + 0.7142857143 0.7142857143x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.7142857143x + x2 = 0.7142857143 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 0.7142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 0.7142857143 + 0.1275510204 Combine like terms: 0.7142857143 + 0.1275510204 = 0.8418367347 0.1275510204 + 0.7142857143x + x2 = 0.8418367347 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 0.8418367347 Calculate the square root of the right side: 0.917516613 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 0.917516613 and -0.917516613.Subproblem 1
x + 0.3571428572 = 0.917516613 Simplifying x + 0.3571428572 = 0.917516613 Reorder the terms: 0.3571428572 + x = 0.917516613 Solving 0.3571428572 + x = 0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 0.917516613 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.917516613 + -0.3571428572 x = 0.917516613 + -0.3571428572 Combine like terms: 0.917516613 + -0.3571428572 = 0.5603737558 x = 0.5603737558 Simplifying x = 0.5603737558Subproblem 2
x + 0.3571428572 = -0.917516613 Simplifying x + 0.3571428572 = -0.917516613 Reorder the terms: 0.3571428572 + x = -0.917516613 Solving 0.3571428572 + x = -0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -0.917516613 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.917516613 + -0.3571428572 x = -0.917516613 + -0.3571428572 Combine like terms: -0.917516613 + -0.3571428572 = -1.2746594702 x = -1.2746594702 Simplifying x = -1.2746594702Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5603737558, -1.2746594702}Solution
x = {0, 0.5603737558, -1.2746594702}
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