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Simplifying 15x4 + 17x2 + -12 = 0 Reorder the terms: -12 + 17x2 + 15x4 = 0 Solving -12 + 17x2 + 15x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8 + 1.133333333x2 + x4 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 1.133333333x2 + 0.8 + x4 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 1.133333333x2 + x4 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1.133333333x2 + x4 = 0 + 0.8 1.133333333x2 + x4 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 1.133333333x2 + x4 = 0.8 The x term is 1.133333333x2. Take half its coefficient (0.5666666665). Square it (0.3211111109) and add it to both sides. Add '0.3211111109' to each side of the equation. 1.133333333x2 + 0.3211111109 + x4 = 0.8 + 0.3211111109 Reorder the terms: 0.3211111109 + 1.133333333x2 + x4 = 0.8 + 0.3211111109 Combine like terms: 0.8 + 0.3211111109 = 1.1211111109 0.3211111109 + 1.133333333x2 + x4 = 1.1211111109 Factor a perfect square on the left side: (x2 + 0.5666666665)(x2 + 0.5666666665) = 1.1211111109 Calculate the square root of the right side: 1.058825345 Break this problem into two subproblems by setting (x2 + 0.5666666665) equal to 1.058825345 and -1.058825345.Subproblem 1
x2 + 0.5666666665 = 1.058825345 Simplifying x2 + 0.5666666665 = 1.058825345 Reorder the terms: 0.5666666665 + x2 = 1.058825345 Solving 0.5666666665 + x2 = 1.058825345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5666666665' to each side of the equation. 0.5666666665 + -0.5666666665 + x2 = 1.058825345 + -0.5666666665 Combine like terms: 0.5666666665 + -0.5666666665 = 0.0000000000 0.0000000000 + x2 = 1.058825345 + -0.5666666665 x2 = 1.058825345 + -0.5666666665 Combine like terms: 1.058825345 + -0.5666666665 = 0.4921586785 x2 = 0.4921586785 Simplifying x2 = 0.4921586785 Take the square root of each side: x = {-0.701540219, 0.701540219}Subproblem 2
x2 + 0.5666666665 = -1.058825345 Simplifying x2 + 0.5666666665 = -1.058825345 Reorder the terms: 0.5666666665 + x2 = -1.058825345 Solving 0.5666666665 + x2 = -1.058825345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5666666665' to each side of the equation. 0.5666666665 + -0.5666666665 + x2 = -1.058825345 + -0.5666666665 Combine like terms: 0.5666666665 + -0.5666666665 = 0.0000000000 0.0000000000 + x2 = -1.058825345 + -0.5666666665 x2 = -1.058825345 + -0.5666666665 Combine like terms: -1.058825345 + -0.5666666665 = -1.6254920115 x2 = -1.6254920115 Simplifying x2 = -1.6254920115 Reorder the terms: 1.6254920115 + x2 = -1.6254920115 + 1.6254920115 Combine like terms: -1.6254920115 + 1.6254920115 = 0.0000000000 1.6254920115 + 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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