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Simplifying 20x2 + 88x + 192 = 0 Reorder the terms: 192 + 88x + 20x2 = 0 Solving 192 + 88x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(48 + 22x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(48 + 22x + 5x2)' equal to zero and attempt to solve: Simplifying 48 + 22x + 5x2 = 0 Solving 48 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 9.6 + 4.4x + x2 = 0 Move the constant term to the right: Add '-9.6' to each side of the equation. 9.6 + 4.4x + -9.6 + x2 = 0 + -9.6 Reorder the terms: 9.6 + -9.6 + 4.4x + x2 = 0 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + 4.4x + x2 = 0 + -9.6 4.4x + x2 = 0 + -9.6 Combine like terms: 0 + -9.6 = -9.6 4.4x + x2 = -9.6 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = -9.6 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = -9.6 + 4.84 Combine like terms: -9.6 + 4.84 = -4.76 4.84 + 4.4x + x2 = -4.76 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = -4.76 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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