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Simplifying (3x2 + 2x + -7) = (5x2 + 5x + 8) Reorder the terms: (-7 + 2x + 3x2) = (5x2 + 5x + 8) Remove parenthesis around (-7 + 2x + 3x2) -7 + 2x + 3x2 = (5x2 + 5x + 8) Reorder the terms: -7 + 2x + 3x2 = (8 + 5x + 5x2) Remove parenthesis around (8 + 5x + 5x2) -7 + 2x + 3x2 = 8 + 5x + 5x2 Solving -7 + 2x + 3x2 = 8 + 5x + 5x2 Solving for variable 'x'. Reorder the terms: -7 + -8 + 2x + -5x + 3x2 + -5x2 = 8 + 5x + 5x2 + -8 + -5x + -5x2 Combine like terms: -7 + -8 = -15 -15 + 2x + -5x + 3x2 + -5x2 = 8 + 5x + 5x2 + -8 + -5x + -5x2 Combine like terms: 2x + -5x = -3x -15 + -3x + 3x2 + -5x2 = 8 + 5x + 5x2 + -8 + -5x + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 -15 + -3x + -2x2 = 8 + 5x + 5x2 + -8 + -5x + -5x2 Reorder the terms: -15 + -3x + -2x2 = 8 + -8 + 5x + -5x + 5x2 + -5x2 Combine like terms: 8 + -8 = 0 -15 + -3x + -2x2 = 0 + 5x + -5x + 5x2 + -5x2 -15 + -3x + -2x2 = 5x + -5x + 5x2 + -5x2 Combine like terms: 5x + -5x = 0 -15 + -3x + -2x2 = 0 + 5x2 + -5x2 -15 + -3x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -15 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 3x + 2x2 = 0 Solving 15 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 1.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 1.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 1.5x + x2 = 0 + -7.5 1.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 1.5x + x2 = -7.5 The x term is 1.5x. 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. 1.5x + 0.5625 + x2 = -7.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -7.5 + 0.5625 Combine like terms: -7.5 + 0.5625 = -6.9375 0.5625 + 1.5x + x2 = -6.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -6.9375 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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