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Simplifying (2x + 1)(4x + -3) + 100x2 + 25 = 0 Reorder the terms: (1 + 2x)(4x + -3) + 100x2 + 25 = 0 Reorder the terms: (1 + 2x)(-3 + 4x) + 100x2 + 25 = 0 Multiply (1 + 2x) * (-3 + 4x) (1(-3 + 4x) + 2x * (-3 + 4x)) + 100x2 + 25 = 0 ((-3 * 1 + 4x * 1) + 2x * (-3 + 4x)) + 100x2 + 25 = 0 ((-3 + 4x) + 2x * (-3 + 4x)) + 100x2 + 25 = 0 (-3 + 4x + (-3 * 2x + 4x * 2x)) + 100x2 + 25 = 0 (-3 + 4x + (-6x + 8x2)) + 100x2 + 25 = 0 Combine like terms: 4x + -6x = -2x (-3 + -2x + 8x2) + 100x2 + 25 = 0 Reorder the terms: -3 + 25 + -2x + 8x2 + 100x2 = 0 Combine like terms: -3 + 25 = 22 22 + -2x + 8x2 + 100x2 = 0 Combine like terms: 8x2 + 100x2 = 108x2 22 + -2x + 108x2 = 0 Solving 22 + -2x + 108x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -1x + 54x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -1x + 54x2)' equal to zero and attempt to solve: Simplifying 11 + -1x + 54x2 = 0 Solving 11 + -1x + 54x2 = 0 Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. 0.2037037037 + -0.01851851852x + x2 = 0 Move the constant term to the right: Add '-0.2037037037' to each side of the equation. 0.2037037037 + -0.01851851852x + -0.2037037037 + x2 = 0 + -0.2037037037 Reorder the terms: 0.2037037037 + -0.2037037037 + -0.01851851852x + x2 = 0 + -0.2037037037 Combine like terms: 0.2037037037 + -0.2037037037 = 0.0000000000 0.0000000000 + -0.01851851852x + x2 = 0 + -0.2037037037 -0.01851851852x + x2 = 0 + -0.2037037037 Combine like terms: 0 + -0.2037037037 = -0.2037037037 -0.01851851852x + x2 = -0.2037037037 The x term is -0.01851851852x. Take half its coefficient (-0.00925925926). Square it (0.00008573388204) and add it to both sides. Add '0.00008573388204' to each side of the equation. -0.01851851852x + 0.00008573388204 + x2 = -0.2037037037 + 0.00008573388204 Reorder the terms: 0.00008573388204 + -0.01851851852x + x2 = -0.2037037037 + 0.00008573388204 Combine like terms: -0.2037037037 + 0.00008573388204 = -0.20361796981796 0.00008573388204 + -0.01851851852x + x2 = -0.20361796981796 Factor a perfect square on the left side: (x + -0.00925925926)(x + -0.00925925926) = -0.20361796981796 Can't calculate square root of the right side. 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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