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Simplifying (3x * 3x * 3x * 3x) + -1(12x * 12x) + 9 = 0 Reorder the terms for easier multiplication: (3 * 3 * 3 * 3x * x * x * x) + -1(12x * 12x) + 9 = 0 Multiply 3 * 3 (9 * 3 * 3x * x * x * x) + -1(12x * 12x) + 9 = 0 Multiply 9 * 3 (27 * 3x * x * x * x) + -1(12x * 12x) + 9 = 0 Multiply 27 * 3 (81x * x * x * x) + -1(12x * 12x) + 9 = 0 Multiply x * x (81x2 * x * x) + -1(12x * 12x) + 9 = 0 Multiply x2 * x (81x3 * x) + -1(12x * 12x) + 9 = 0 Multiply x3 * x (81x4) + -1(12x * 12x) + 9 = 0 Reorder the terms for easier multiplication: (81x4) + -1(12 * 12x * x) + 9 = 0 Multiply 12 * 12 (81x4) + -1(144x * x) + 9 = 0 Multiply x * x (81x4) + -1(144x2) + 9 = 0 Remove parenthesis around (144x2) (81x4) + -1 * 144x2 + 9 = 0 Multiply -1 * 144 (81x4) + -144x2 + 9 = 0 Reorder the terms: 9 + -144x2 + (81x4) = 0 Solving 9 + -144x2 + (81x4) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + -16x2 + (9x4)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -16x2 + (9x4))' equal to zero and attempt to solve: Simplifying 1 + -16x2 + (9x4) = 0 Solving 1 + -16x2 + (9x4) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -1.777777778x2 + x4 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -1.777777778x2 + -0.1111111111 + x4 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -1.777777778x2 + x4 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -1.777777778x2 + x4 = 0 + -0.1111111111 -1.777777778x2 + x4 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -1.777777778x2 + x4 = -0.1111111111 The x term is -1.777777778x2. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778x2 + 0.7901234570 + x4 = -0.1111111111 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x2 + x4 = -0.1111111111 + 0.7901234570 Combine like terms: -0.1111111111 + 0.7901234570 = 0.6790123459 0.7901234570 + -1.777777778x2 + x4 = 0.6790123459 Factor a perfect square on the left side: ((x2) + -0.888888889)((x2) + -0.888888889) = 0.6790123459 Calculate the square root of the right side: 0.824022054 Break this problem into two subproblems by setting ((x2) + -0.888888889) equal to 0.824022054 and -0.824022054.Subproblem 1
(x2) + -0.888888889 = 0.824022054 Simplifying (x2) + -0.888888889 = 0.824022054 x2 + -0.888888889 = 0.824022054 Reorder the terms: -0.888888889 + x2 = 0.824022054 Solving -0.888888889 + x2 = 0.824022054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x2 = 0.824022054 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x2 = 0.824022054 + 0.888888889 x2 = 0.824022054 + 0.888888889 Combine like terms: 0.824022054 + 0.888888889 = 1.712910943 x2 = 1.712910943 Simplifying x2 = 1.712910943 Take the square root of each side: x = {-1.308782237, 1.308782237}Subproblem 2
(x2) + -0.888888889 = -0.824022054 Simplifying (x2) + -0.888888889 = -0.824022054 x2 + -0.888888889 = -0.824022054 Reorder the terms: -0.888888889 + x2 = -0.824022054 Solving -0.888888889 + x2 = -0.824022054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x2 = -0.824022054 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x2 = -0.824022054 + 0.888888889 x2 = -0.824022054 + 0.888888889 Combine like terms: -0.824022054 + 0.888888889 = 0.064866835 x2 = 0.064866835 Simplifying x2 = 0.064866835 Take the square root of each side: x = {-0.254689684, 0.254689684}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.308782237, 1.308782237, -0.254689684, 0.254689684}Solution
x = {-1.308782237, 1.308782237, -0.254689684, 0.254689684}
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