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Simplifying 6x4 + 17x2 + 4 = 0 Reorder the terms: 4 + 17x2 + 6x4 = 0 Solving 4 + 17x2 + 6x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 2.833333333x2 + x4 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 2.833333333x2 + -0.6666666667 + x4 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 2.833333333x2 + x4 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 2.833333333x2 + x4 = 0 + -0.6666666667 2.833333333x2 + x4 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 2.833333333x2 + x4 = -0.6666666667 The x term is 2.833333333x2. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333x2 + 2.006944445 + x4 = -0.6666666667 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333x2 + x4 = -0.6666666667 + 2.006944445 Combine like terms: -0.6666666667 + 2.006944445 = 1.3402777783 2.006944445 + 2.833333333x2 + x4 = 1.3402777783 Factor a perfect square on the left side: (x2 + 1.416666667)(x2 + 1.416666667) = 1.3402777783 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x2 + 1.416666667) equal to 1.157703666 and -1.157703666.Subproblem 1
x2 + 1.416666667 = 1.157703666 Simplifying x2 + 1.416666667 = 1.157703666 Reorder the terms: 1.416666667 + x2 = 1.157703666 Solving 1.416666667 + x2 = 1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x2 = 1.157703666 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x2 = 1.157703666 + -1.416666667 x2 = 1.157703666 + -1.416666667 Combine like terms: 1.157703666 + -1.416666667 = -0.258963001 x2 = -0.258963001 Simplifying x2 = -0.258963001 Reorder the terms: 0.258963001 + x2 = -0.258963001 + 0.258963001 Combine like terms: -0.258963001 + 0.258963001 = 0.000000000 0.258963001 + 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 + 1.416666667 = -1.157703666 Simplifying x2 + 1.416666667 = -1.157703666 Reorder the terms: 1.416666667 + x2 = -1.157703666 Solving 1.416666667 + x2 = -1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x2 = -1.157703666 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x2 = -1.157703666 + -1.416666667 x2 = -1.157703666 + -1.416666667 Combine like terms: -1.157703666 + -1.416666667 = -2.574370333 x2 = -2.574370333 Simplifying x2 = -2.574370333 Reorder the terms: 2.574370333 + x2 = -2.574370333 + 2.574370333 Combine like terms: -2.574370333 + 2.574370333 = 0.000000000 2.574370333 + 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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