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Simplifying 9x4 + 10x2 + -15 = 0 Reorder the terms: -15 + 10x2 + 9x4 = 0 Solving -15 + 10x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + 1.111111111x2 + x4 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 1.111111111x2 + 1.666666667 + x4 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 1.111111111x2 + x4 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 1.111111111x2 + x4 = 0 + 1.666666667 1.111111111x2 + x4 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 1.111111111x2 + x4 = 1.666666667 The x term is 1.111111111x2. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x2 + 0.3086419752 + x4 = 1.666666667 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x2 + x4 = 1.666666667 + 0.3086419752 Combine like terms: 1.666666667 + 0.3086419752 = 1.9753086422 0.3086419752 + 1.111111111x2 + x4 = 1.9753086422 Factor a perfect square on the left side: (x2 + 0.5555555555)(x2 + 0.5555555555) = 1.9753086422 Calculate the square root of the right side: 1.405456738 Break this problem into two subproblems by setting (x2 + 0.5555555555) equal to 1.405456738 and -1.405456738.Subproblem 1
x2 + 0.5555555555 = 1.405456738 Simplifying x2 + 0.5555555555 = 1.405456738 Reorder the terms: 0.5555555555 + x2 = 1.405456738 Solving 0.5555555555 + x2 = 1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x2 = 1.405456738 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x2 = 1.405456738 + -0.5555555555 x2 = 1.405456738 + -0.5555555555 Combine like terms: 1.405456738 + -0.5555555555 = 0.8499011825 x2 = 0.8499011825 Simplifying x2 = 0.8499011825 Take the square root of each side: x = {-0.921900853, 0.921900853}Subproblem 2
x2 + 0.5555555555 = -1.405456738 Simplifying x2 + 0.5555555555 = -1.405456738 Reorder the terms: 0.5555555555 + x2 = -1.405456738 Solving 0.5555555555 + x2 = -1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x2 = -1.405456738 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x2 = -1.405456738 + -0.5555555555 x2 = -1.405456738 + -0.5555555555 Combine like terms: -1.405456738 + -0.5555555555 = -1.9610122935 x2 = -1.9610122935 Simplifying x2 = -1.9610122935 Reorder the terms: 1.9610122935 + x2 = -1.9610122935 + 1.9610122935 Combine like terms: -1.9610122935 + 1.9610122935 = 0.0000000000 1.9610122935 + x2 = 0.0000000000 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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