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Simplifying 9x4 + 16x2 = -1 Reorder the terms: 16x2 + 9x4 = -1 Solving 16x2 + 9x4 = -1 Solving for variable 'x'. Reorder the terms: 1 + 16x2 + 9x4 = -1 + 1 Combine like terms: -1 + 1 = 0 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 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 Reorder the terms: 0.064866835 + x2 = -0.064866835 + 0.064866835 Combine like terms: -0.064866835 + 0.064866835 = 0.000000000 0.064866835 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 0.888888889 = -0.824022054 Simplifying 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 Reorder the terms: 1.712910943 + x2 = -1.712910943 + 1.712910943 Combine like terms: -1.712910943 + 1.712910943 = 0.000000000 1.712910943 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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