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Simplifying 0 = (3x2 + 5x + 2) + (4 + 2x) + (5x2 + 7) Reorder the terms: 0 = (2 + 5x + 3x2) + (4 + 2x) + (5x2 + 7) Remove parenthesis around (2 + 5x + 3x2) 0 = 2 + 5x + 3x2 + (4 + 2x) + (5x2 + 7) Remove parenthesis around (4 + 2x) 0 = 2 + 5x + 3x2 + 4 + 2x + (5x2 + 7) Reorder the terms: 0 = 2 + 5x + 3x2 + 4 + 2x + (7 + 5x2) Remove parenthesis around (7 + 5x2) 0 = 2 + 5x + 3x2 + 4 + 2x + 7 + 5x2 Reorder the terms: 0 = 2 + 4 + 7 + 5x + 2x + 3x2 + 5x2 Combine like terms: 2 + 4 = 6 0 = 6 + 7 + 5x + 2x + 3x2 + 5x2 Combine like terms: 6 + 7 = 13 0 = 13 + 5x + 2x + 3x2 + 5x2 Combine like terms: 5x + 2x = 7x 0 = 13 + 7x + 3x2 + 5x2 Combine like terms: 3x2 + 5x2 = 8x2 0 = 13 + 7x + 8x2 Solving 0 = 13 + 7x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -13 = -13 -13 + -7x + -8x2 = 13 + 7x + 8x2 + -13 + -7x + -8x2 Reorder the terms: -13 + -7x + -8x2 = 13 + -13 + 7x + -7x + 8x2 + -8x2 Combine like terms: 13 + -13 = 0 -13 + -7x + -8x2 = 0 + 7x + -7x + 8x2 + -8x2 -13 + -7x + -8x2 = 7x + -7x + 8x2 + -8x2 Combine like terms: 7x + -7x = 0 -13 + -7x + -8x2 = 0 + 8x2 + -8x2 -13 + -7x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -13 + -7x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 7x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 7x + 8x2)' equal to zero and attempt to solve: Simplifying 13 + 7x + 8x2 = 0 Solving 13 + 7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.625 + 0.875x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + 0.875x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + 0.875x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + 0.875x + x2 = 0 + -1.625 0.875x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 0.875x + x2 = -1.625 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = -1.625 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = -1.625 + 0.19140625 Combine like terms: -1.625 + 0.19140625 = -1.43359375 0.19140625 + 0.875x + x2 = -1.43359375 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = -1.43359375 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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