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Simplifying (5x3 + -3x2 + 7x) + (9x3 + 9x2 + -13x) = 0 Reorder the terms: (7x + -3x2 + 5x3) + (9x3 + 9x2 + -13x) = 0 Remove parenthesis around (7x + -3x2 + 5x3) 7x + -3x2 + 5x3 + (9x3 + 9x2 + -13x) = 0 Reorder the terms: 7x + -3x2 + 5x3 + (-13x + 9x2 + 9x3) = 0 Remove parenthesis around (-13x + 9x2 + 9x3) 7x + -3x2 + 5x3 + -13x + 9x2 + 9x3 = 0 Reorder the terms: 7x + -13x + -3x2 + 9x2 + 5x3 + 9x3 = 0 Combine like terms: 7x + -13x = -6x -6x + -3x2 + 9x2 + 5x3 + 9x3 = 0 Combine like terms: -3x2 + 9x2 = 6x2 -6x + 6x2 + 5x3 + 9x3 = 0 Combine like terms: 5x3 + 9x3 = 14x3 -6x + 6x2 + 14x3 = 0 Solving -6x + 6x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + 3x + 7x2) = 0 Ignore the factor 2.Subproblem 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 '(-3 + 3x + 7x2)' equal to zero and attempt to solve: Simplifying -3 + 3x + 7x2 = 0 Solving -3 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.4285714286x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.4285714286x + x2 = 0 + 0.4285714286 0.4285714286x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.4285714286x + x2 = 0.4285714286 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 0.4285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 0.4285714286 + 0.04591836735 Combine like terms: 0.4285714286 + 0.04591836735 = 0.47448979595 0.04591836735 + 0.4285714286x + x2 = 0.47448979595 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 0.47448979595 Calculate the square root of the right side: 0.688832197 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 0.688832197 and -0.688832197.Subproblem 1
x + 0.2142857143 = 0.688832197 Simplifying x + 0.2142857143 = 0.688832197 Reorder the terms: 0.2142857143 + x = 0.688832197 Solving 0.2142857143 + x = 0.688832197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 0.688832197 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 0.688832197 + -0.2142857143 x = 0.688832197 + -0.2142857143 Combine like terms: 0.688832197 + -0.2142857143 = 0.4745464827 x = 0.4745464827 Simplifying x = 0.4745464827Subproblem 2
x + 0.2142857143 = -0.688832197 Simplifying x + 0.2142857143 = -0.688832197 Reorder the terms: 0.2142857143 + x = -0.688832197 Solving 0.2142857143 + x = -0.688832197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -0.688832197 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -0.688832197 + -0.2142857143 x = -0.688832197 + -0.2142857143 Combine like terms: -0.688832197 + -0.2142857143 = -0.9031179113 x = -0.9031179113 Simplifying x = -0.9031179113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4745464827, -0.9031179113}Solution
x = {0, 0.4745464827, -0.9031179113}
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