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Simplifying 10x4 + 15x2 + 2 = 0 Reorder the terms: 2 + 15x2 + 10x4 = 0 Solving 2 + 15x2 + 10x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.2 + 1.5x2 + x4 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.5x2 + -0.2 + x4 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.5x2 + x4 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.5x2 + x4 = 0 + -0.2 1.5x2 + x4 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.5x2 + x4 = -0.2 The x term is 1.5x2. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x2 + 0.5625 + x4 = -0.2 + 0.5625 Reorder the terms: 0.5625 + 1.5x2 + x4 = -0.2 + 0.5625 Combine like terms: -0.2 + 0.5625 = 0.3625 0.5625 + 1.5x2 + x4 = 0.3625 Factor a perfect square on the left side: (x2 + 0.75)(x2 + 0.75) = 0.3625 Calculate the square root of the right side: 0.602079729 Break this problem into two subproblems by setting (x2 + 0.75) equal to 0.602079729 and -0.602079729.Subproblem 1
x2 + 0.75 = 0.602079729 Simplifying x2 + 0.75 = 0.602079729 Reorder the terms: 0.75 + x2 = 0.602079729 Solving 0.75 + x2 = 0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = 0.602079729 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = 0.602079729 + -0.75 x2 = 0.602079729 + -0.75 Combine like terms: 0.602079729 + -0.75 = -0.147920271 x2 = -0.147920271 Simplifying x2 = -0.147920271 Reorder the terms: 0.147920271 + x2 = -0.147920271 + 0.147920271 Combine like terms: -0.147920271 + 0.147920271 = 0.000000000 0.147920271 + 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 + 0.75 = -0.602079729 Simplifying x2 + 0.75 = -0.602079729 Reorder the terms: 0.75 + x2 = -0.602079729 Solving 0.75 + x2 = -0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = -0.602079729 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = -0.602079729 + -0.75 x2 = -0.602079729 + -0.75 Combine like terms: -0.602079729 + -0.75 = -1.352079729 x2 = -1.352079729 Simplifying x2 = -1.352079729 Reorder the terms: 1.352079729 + x2 = -1.352079729 + 1.352079729 Combine like terms: -1.352079729 + 1.352079729 = 0.000000000 1.352079729 + 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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