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Simplifying 20x2 + 30x + 68 = 0 Reorder the terms: 68 + 30x + 20x2 = 0 Solving 68 + 30x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(34 + 15x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + 15x + 10x2)' equal to zero and attempt to solve: Simplifying 34 + 15x + 10x2 = 0 Solving 34 + 15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3.4 + 1.5x + x2 = 0.0 Move the constant term to the right: Add '-3.4' to each side of the equation. 3.4 + 1.5x + -3.4 + x2 = 0.0 + -3.4 Reorder the terms: 3.4 + -3.4 + 1.5x + x2 = 0.0 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + 1.5x + x2 = 0.0 + -3.4 1.5x + x2 = 0.0 + -3.4 Combine like terms: 0.0 + -3.4 = -3.4 1.5x + x2 = -3.4 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 = -3.4 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -3.4 + 0.5625 Combine like terms: -3.4 + 0.5625 = -2.8375 0.5625 + 1.5x + x2 = -2.8375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -2.8375 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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