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Simplifying -7x + 5x2 + -5x3 + 8x + 3x2 + -7x3 + x3 = 0 Reorder the terms: -7x + 8x + 5x2 + 3x2 + -5x3 + -7x3 + x3 = 0 Combine like terms: -7x + 8x = 1x 1x + 5x2 + 3x2 + -5x3 + -7x3 + x3 = 0 Combine like terms: 5x2 + 3x2 = 8x2 1x + 8x2 + -5x3 + -7x3 + x3 = 0 Combine like terms: -5x3 + -7x3 = -12x3 1x + 8x2 + -12x3 + x3 = 0 Combine like terms: -12x3 + x3 = -11x3 1x + 8x2 + -11x3 = 0 Solving 1x + 8x2 + -11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 8x + -11x2) = 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 '(1 + 8x + -11x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + -11x2 = 0 Solving 1 + 8x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.09090909091 + -0.7272727273x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.7272727273x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.7272727273x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.7272727273x + x2 = 0 + 0.09090909091 -0.7272727273x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.7272727273x + x2 = 0.09090909091 The x term is -0.7272727273x. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273x + 0.1322314050 + x2 = 0.09090909091 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273x + x2 = 0.09090909091 + 0.1322314050 Combine like terms: 0.09090909091 + 0.1322314050 = 0.22314049591 0.1322314050 + -0.7272727273x + x2 = 0.22314049591 Factor a perfect square on the left side: (x + -0.3636363637)(x + -0.3636363637) = 0.22314049591 Calculate the square root of the right side: 0.472377493 Break this problem into two subproblems by setting (x + -0.3636363637) equal to 0.472377493 and -0.472377493.Subproblem 1
x + -0.3636363637 = 0.472377493 Simplifying x + -0.3636363637 = 0.472377493 Reorder the terms: -0.3636363637 + x = 0.472377493 Solving -0.3636363637 + x = 0.472377493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = 0.472377493 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = 0.472377493 + 0.3636363637 x = 0.472377493 + 0.3636363637 Combine like terms: 0.472377493 + 0.3636363637 = 0.8360138567 x = 0.8360138567 Simplifying x = 0.8360138567Subproblem 2
x + -0.3636363637 = -0.472377493 Simplifying x + -0.3636363637 = -0.472377493 Reorder the terms: -0.3636363637 + x = -0.472377493 Solving -0.3636363637 + x = -0.472377493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = -0.472377493 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = -0.472377493 + 0.3636363637 x = -0.472377493 + 0.3636363637 Combine like terms: -0.472377493 + 0.3636363637 = -0.1087411293 x = -0.1087411293 Simplifying x = -0.1087411293Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8360138567, -0.1087411293}Solution
x = {0, 0.8360138567, -0.1087411293}
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