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Simplifying 0 = 9x4 + -160x2 + 232 Reorder the terms: 0 = 232 + -160x2 + 9x4 Solving 0 = 232 + -160x2 + 9x4 Solving for variable 'x'. Combine like terms: 0 + -232 = -232 -232 + 160x2 + -9x4 = 232 + -160x2 + 9x4 + -232 + 160x2 + -9x4 Reorder the terms: -232 + 160x2 + -9x4 = 232 + -232 + -160x2 + 160x2 + 9x4 + -9x4 Combine like terms: 232 + -232 = 0 -232 + 160x2 + -9x4 = 0 + -160x2 + 160x2 + 9x4 + -9x4 -232 + 160x2 + -9x4 = -160x2 + 160x2 + 9x4 + -9x4 Combine like terms: -160x2 + 160x2 = 0 -232 + 160x2 + -9x4 = 0 + 9x4 + -9x4 -232 + 160x2 + -9x4 = 9x4 + -9x4 Combine like terms: 9x4 + -9x4 = 0 -232 + 160x2 + -9x4 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 25.77777778 + -17.77777778x2 + x4 = 0 Move the constant term to the right: Add '-25.77777778' to each side of the equation. 25.77777778 + -17.77777778x2 + -25.77777778 + x4 = 0 + -25.77777778 Reorder the terms: 25.77777778 + -25.77777778 + -17.77777778x2 + x4 = 0 + -25.77777778 Combine like terms: 25.77777778 + -25.77777778 = 0.00000000 0.00000000 + -17.77777778x2 + x4 = 0 + -25.77777778 -17.77777778x2 + x4 = 0 + -25.77777778 Combine like terms: 0 + -25.77777778 = -25.77777778 -17.77777778x2 + x4 = -25.77777778 The x term is -17.77777778x2. Take half its coefficient (-8.88888889). Square it (79.01234570) and add it to both sides. Add '79.01234570' to each side of the equation. -17.77777778x2 + 79.01234570 + x4 = -25.77777778 + 79.01234570 Reorder the terms: 79.01234570 + -17.77777778x2 + x4 = -25.77777778 + 79.01234570 Combine like terms: -25.77777778 + 79.01234570 = 53.23456792 79.01234570 + -17.77777778x2 + x4 = 53.23456792 Factor a perfect square on the left side: (x2 + -8.88888889)(x2 + -8.88888889) = 53.23456792 Calculate the square root of the right side: 7.296202294 Break this problem into two subproblems by setting (x2 + -8.88888889) equal to 7.296202294 and -7.296202294.Subproblem 1
x2 + -8.88888889 = 7.296202294 Simplifying x2 + -8.88888889 = 7.296202294 Reorder the terms: -8.88888889 + x2 = 7.296202294 Solving -8.88888889 + x2 = 7.296202294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.88888889' to each side of the equation. -8.88888889 + 8.88888889 + x2 = 7.296202294 + 8.88888889 Combine like terms: -8.88888889 + 8.88888889 = 0.00000000 0.00000000 + x2 = 7.296202294 + 8.88888889 x2 = 7.296202294 + 8.88888889 Combine like terms: 7.296202294 + 8.88888889 = 16.185091184 x2 = 16.185091184 Simplifying x2 = 16.185091184 Take the square root of each side: x = {-4.023069871, 4.023069871}Subproblem 2
x2 + -8.88888889 = -7.296202294 Simplifying x2 + -8.88888889 = -7.296202294 Reorder the terms: -8.88888889 + x2 = -7.296202294 Solving -8.88888889 + x2 = -7.296202294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.88888889' to each side of the equation. -8.88888889 + 8.88888889 + x2 = -7.296202294 + 8.88888889 Combine like terms: -8.88888889 + 8.88888889 = 0.00000000 0.00000000 + x2 = -7.296202294 + 8.88888889 x2 = -7.296202294 + 8.88888889 Combine like terms: -7.296202294 + 8.88888889 = 1.592686596 x2 = 1.592686596 Simplifying x2 = 1.592686596 Take the square root of each side: x = {-1.262016876, 1.262016876}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.023069871, 4.023069871, -1.262016876, 1.262016876}
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