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Simplifying 0 = 2x2 + 3x + 5 Reorder the terms: 0 = 5 + 3x + 2x2 Solving 0 = 5 + 3x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -3x + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2 Reorder the terms: -5 + -3x + -2x2 = 5 + -5 + 3x + -3x + 2x2 + -2x2 Combine like terms: 5 + -5 = 0 -5 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2 -5 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 -5 + -3x + -2x2 = 0 + 2x2 + -2x2 -5 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 2x2 = 0 Solving 5 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 1.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 1.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 1.5x + x2 = 0 + -2.5 1.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 1.5x + x2 = -2.5 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 = -2.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + 1.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.9375 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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